Explanation Given information: Given definite integral is ∫ 0 π 4 ( sin t + cos t ) d t Calculation: Solving the indefinite integral: ∫ ( sin t + cos t ) d t The antiderivative of a function of the form ( a + b ) is given by ∫ ( a + b ) d x = ∫ a d x + ∫ b d x The antiderivative of a function of the form cos θ is given by ∫ cos θ d θ = sin θ The antiderivative of a function of the form sin θ is given by ∫ sin θ d θ = − cos θ Using the above-mentionedrules, ∫ ( sin t + cos t ) d t = ∫ sin t d t + ∫ cos t d t ∫ ( sin t + cos t ) d t = − cos t + sin t + c Where C is a constant

Applied Calculus, 6e WileyPLUS + Loose-leaf

6th Edition

ISBN: 9781119408901

Author: Deborah Hughes-Hallett, Andrew M. Gleason, Patti Frazer Lock, Daniel E. Flath

Publisher: Wiley (WileyPLUS Products)

See similar textbooks

Concept explainers

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence t…

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.

Videos

Question

Chapter 6.3, Problem 18P

To determine

To evaluate the definite integral using the Fundamental Theorem.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 6.3, Problem 17P

Chapter 6.3, Problem 19P

Students have asked these similar questions

Use Euler's method to numerically integrate dy dx -2x+12x² - 20x +8.5 from x=0 to x=4 with a step size of 0.5. The initial condition at x=0 is y=1. Recall that the exact solution is given by y = -0.5x+4x³- 10x² + 8.5x+1

Find an equation of the line tangent to the graph of f(x) = (5x-9)(x+4) at (2,6).

Find the point on the graph of the given function at which the slope of the tangent line is the given slope. 2 f(x)=8x²+4x-7; slope of the tangent line = -3

Chapter 6 Solutions

Applied Calculus, 6e WileyPLUS + Loose-leaf

Ch. 6.1 - Prob. 1P Ch. 6.1 - Prob. 2P Ch. 6.1 - Prob. 3P Ch. 6.1 - Prob. 4P Ch. 6.1 - Prob. 5P Ch. 6.1 - Prob. 6P Ch. 6.1 - Prob. 7P Ch. 6.1 - Prob. 8P Ch. 6.1 - Prob. 9P Ch. 6.1 - Prob. 10P

Ch. 6.1 - Prob. 11P Ch. 6.1 - Prob. 12P Ch. 6.1 - Prob. 13P Ch. 6.1 - Prob. 14P Ch. 6.1 - Prob. 15P Ch. 6.1 - Prob. 16P Ch. 6.1 - Prob. 17P Ch. 6.1 - Prob. 18P Ch. 6.1 - Prob. 19P Ch. 6.1 - Prob. 20P Ch. 6.1 - Prob. 21P Ch. 6.1 - Prob. 22P Ch. 6.1 - Prob. 23P Ch. 6.1 - Prob. 24P Ch. 6.1 - Prob. 25P Ch. 6.1 - Prob. 26P Ch. 6.1 - Prob. 27P Ch. 6.1 - Prob. 28P Ch. 6.1 - Prob. 29P Ch. 6.1 - Prob. 30P Ch. 6.1 - Prob. 31P Ch. 6.1 - Prob. 32P Ch. 6.1 - Prob. 33P Ch. 6.1 - Prob. 34P Ch. 6.1 - Prob. 35P Ch. 6.1 - Prob. 36P Ch. 6.1 - Prob. 37P Ch. 6.1 - Prob. 38P Ch. 6.1 - Prob. 39P Ch. 6.1 - Prob. 40P Ch. 6.1 - Prob. 41P Ch. 6.1 - Prob. 42P Ch. 6.1 - Prob. 43P Ch. 6.1 - Prob. 44P Ch. 6.2 - Prob. 1P Ch. 6.2 - Prob. 2P Ch. 6.2 - Prob. 3P Ch. 6.2 - Prob. 4P Ch. 6.2 - Prob. 5P Ch. 6.2 - Prob. 6P Ch. 6.2 - Prob. 7P Ch. 6.2 - Prob. 8P Ch. 6.2 - Prob. 9P Ch. 6.2 - Prob. 10P Ch. 6.2 - Prob. 11P Ch. 6.2 - Prob. 12P Ch. 6.2 - Prob. 13P Ch. 6.2 - Prob. 14P Ch. 6.2 - Prob. 15P Ch. 6.2 - Prob. 16P Ch. 6.2 - Prob. 17P Ch. 6.2 - Prob. 18P Ch. 6.2 - Prob. 19P Ch. 6.2 - Prob. 20P Ch. 6.2 - Prob. 21P Ch. 6.2 - Prob. 22P Ch. 6.2 - Prob. 23P Ch. 6.2 - Prob. 24P Ch. 6.2 - Prob. 25P Ch. 6.2 - Prob. 26P Ch. 6.2 - Prob. 27P Ch. 6.2 - Prob. 28P Ch. 6.2 - Prob. 29P Ch. 6.2 - Prob. 30P Ch. 6.2 - Prob. 31P Ch. 6.2 - Prob. 32P Ch. 6.2 - Prob. 33P Ch. 6.2 - Prob. 34P Ch. 6.2 - Prob. 35P Ch. 6.2 - Prob. 36P Ch. 6.2 - Prob. 37P Ch. 6.2 - Prob. 38P Ch. 6.2 - Prob. 39P Ch. 6.2 - Prob. 40P Ch. 6.2 - Prob. 41P Ch. 6.2 - Prob. 42P Ch. 6.2 - Prob. 43P Ch. 6.2 - Prob. 44P Ch. 6.2 - Prob. 45P Ch. 6.2 - Prob. 46P Ch. 6.2 - Prob. 47P Ch. 6.2 - Prob. 48P Ch. 6.2 - Prob. 49P Ch. 6.2 - Prob. 50P Ch. 6.2 - Prob. 51P Ch. 6.2 - Prob. 52P Ch. 6.2 - Prob. 53P Ch. 6.2 - Prob. 54P Ch. 6.2 - Prob. 55P Ch. 6.2 - Prob. 56P Ch. 6.2 - Prob. 57P Ch. 6.2 - Prob. 58P Ch. 6.2 - Prob. 59P Ch. 6.2 - Prob. 60P Ch. 6.2 - Prob. 61P Ch. 6.2 - Prob. 62P Ch. 6.2 - Prob. 63P Ch. 6.2 - Prob. 64P Ch. 6.2 - Prob. 65P Ch. 6.2 - Prob. 66P Ch. 6.2 - Prob. 67P Ch. 6.2 - Prob. 68P Ch. 6.2 - Prob. 69P Ch. 6.2 - Prob. 70P Ch. 6.2 - Prob. 71P Ch. 6.2 - Prob. 72P Ch. 6.2 - Prob. 73P Ch. 6.2 - Prob. 74P Ch. 6.2 - Prob. 75P Ch. 6.2 - Prob. 76P Ch. 6.2 - Prob. 77P Ch. 6.2 - Prob. 78P Ch. 6.2 - Prob. 79P Ch. 6.2 - Prob. 80P Ch. 6.2 - Prob. 81P Ch. 6.2 - Prob. 82P Ch. 6.2 - Prob. 83P Ch. 6.2 - Prob. 84P Ch. 6.2 - Prob. 85P Ch. 6.2 - Prob. 86P Ch. 6.2 - Prob. 87P Ch. 6.2 - Prob. 88P Ch. 6.2 - Prob. 89P Ch. 6.2 - Prob. 90P Ch. 6.2 - Prob. 91P Ch. 6.2 - Prob. 92P Ch. 6.2 - Prob. 93P Ch. 6.2 - Prob. 94P Ch. 6.2 - Prob. 95P Ch. 6.3 - Prob. 1P Ch. 6.3 - Prob. 2P Ch. 6.3 - Prob. 3P Ch. 6.3 - Prob. 4P Ch. 6.3 - Prob. 5P Ch. 6.3 - Prob. 6P Ch. 6.3 - Prob. 7P Ch. 6.3 - Prob. 8P Ch. 6.3 - Prob. 9P Ch. 6.3 - Prob. 10P Ch. 6.3 - Prob. 11P Ch. 6.3 - Prob. 12P Ch. 6.3 - Prob. 13P Ch. 6.3 - Prob. 14P Ch. 6.3 - Prob. 15P Ch. 6.3 - Prob. 16P Ch. 6.3 - Prob. 17P Ch. 6.3 - Prob. 18P Ch. 6.3 - Prob. 19P Ch. 6.3 - Prob. 20P Ch. 6.3 - Prob. 21P Ch. 6.3 - Prob. 22P Ch. 6.3 - Prob. 23P Ch. 6.3 - Prob. 24P Ch. 6.3 - Prob. 25P Ch. 6.3 - Prob. 26P Ch. 6.3 - Prob. 27P Ch. 6.3 - Prob. 28P Ch. 6.3 - Prob. 29P Ch. 6.3 - Prob. 30P Ch. 6.3 - Prob. 31P Ch. 6.3 - Prob. 32P Ch. 6.3 - Prob. 33P Ch. 6.3 - Prob. 34P Ch. 6.3 - Prob. 35P Ch. 6.3 - Prob. 36P Ch. 6.3 - Prob. 37P Ch. 6.3 - Prob. 38P Ch. 6.3 - Prob. 39P Ch. 6.3 - Prob. 40P Ch. 6.3 - Prob. 41P Ch. 6.4 - Prob. 1P Ch. 6.4 - Prob. 2P Ch. 6.4 - Prob. 3P Ch. 6.4 - Prob. 4P Ch. 6.4 - Prob. 5P Ch. 6.4 - Prob. 6P Ch. 6.4 - Prob. 7P Ch. 6.4 - Prob. 8P Ch. 6.4 - Prob. 9P Ch. 6.4 - Prob. 10P Ch. 6.4 - Prob. 11P Ch. 6.4 - Prob. 12P Ch. 6.4 - Prob. 13P Ch. 6.4 - Prob. 14P Ch. 6.4 - Prob. 15P Ch. 6.4 - Prob. 16P Ch. 6.4 - Prob. 17P Ch. 6.4 - Prob. 18P Ch. 6.4 - Prob. 19P Ch. 6.5 - Prob. 1P Ch. 6.5 - Prob. 2P Ch. 6.5 - Prob. 3P Ch. 6.5 - Prob. 4P Ch. 6.5 - Prob. 5P Ch. 6.5 - Prob. 6P Ch. 6.5 - Prob. 7P Ch. 6.5 - Prob. 8P Ch. 6.5 - Prob. 9P Ch. 6.5 - Prob. 10P Ch. 6.5 - Prob. 11P Ch. 6.5 - Prob. 12P Ch. 6.5 - Prob. 13P Ch. 6.5 - Prob. 14P Ch. 6.5 - Prob. 15P Ch. 6.5 - Prob. 16P Ch. 6.5 - Prob. 17P Ch. 6.5 - Prob. 18P Ch. 6.5 - Prob. 19P Ch. 6.5 - Prob. 20P Ch. 6.5 - Prob. 21P Ch. 6.5 - Prob. 22P Ch. 6.5 - Prob. 23P Ch. 6.5 - Prob. 24P Ch. 6.6 - Prob. 1P Ch. 6.6 - Prob. 2P Ch. 6.6 - Prob. 3P Ch. 6.6 - Prob. 4P Ch. 6.6 - Prob. 5P Ch. 6.6 - Prob. 6P Ch. 6.6 - Prob. 7P Ch. 6.6 - Prob. 8P Ch. 6.6 - Prob. 9P Ch. 6.6 - Prob. 10P Ch. 6.6 - Prob. 11P Ch. 6.6 - Prob. 12P Ch. 6.6 - Prob. 13P Ch. 6.6 - Prob. 14P Ch. 6.6 - Prob. 15P Ch. 6.6 - Prob. 16P Ch. 6.6 - Prob. 17P Ch. 6.6 - Prob. 18P Ch. 6.6 - Prob. 19P Ch. 6.6 - Prob. 20P Ch. 6.6 - Prob. 21P Ch. 6.6 - Prob. 22P Ch. 6.6 - Prob. 23P Ch. 6.6 - Prob. 24P Ch. 6.6 - Prob. 25P Ch. 6.6 - Prob. 26P Ch. 6.6 - Prob. 27P Ch. 6.6 - Prob. 28P Ch. 6.6 - Prob. 29P Ch. 6.6 - Prob. 30P Ch. 6.6 - Prob. 31P Ch. 6.6 - Prob. 32P Ch. 6.6 - Prob. 33P Ch. 6.6 - Prob. 34P Ch. 6.6 - Prob. 35P Ch. 6.6 - Prob. 36P Ch. 6.6 - Prob. 37P Ch. 6.6 - Prob. 38P Ch. 6.6 - Prob. 39P Ch. 6.6 - Prob. 40P Ch. 6.6 - Prob. 41P Ch. 6.6 - Prob. 42P Ch. 6.6 - Prob. 43P Ch. 6.6 - Prob. 44P Ch. 6.6 - Prob. 45P Ch. 6.6 - Prob. 46P Ch. 6.6 - Prob. 47P Ch. 6.6 - Prob. 48P Ch. 6.6 - Prob. 49P Ch. 6.6 - Prob. 50P Ch. 6.6 - Prob. 51P Ch. 6.6 - Prob. 52P Ch. 6.6 - Prob. 53P Ch. 6.6 - Prob. 54P Ch. 6.6 - Prob. 55P Ch. 6.6 - Prob. 56P Ch. 6.6 - Prob. 57P Ch. 6.6 - Prob. 58P Ch. 6.6 - Prob. 59P Ch. 6.6 - Prob. 60P Ch. 6.6 - Prob. 61P Ch. 6.6 - Prob. 62P Ch. 6.6 - Prob. 63P Ch. 6.6 - Prob. 64P Ch. 6.6 - Prob. 65P Ch. 6.6 - Prob. 66P Ch. 6.6 - Prob. 67P Ch. 6.6 - Prob. 68P Ch. 6.7 - Prob. 1P Ch. 6.7 - Prob. 2P Ch. 6.7 - Prob. 3P Ch. 6.7 - Prob. 4P Ch. 6.7 - Prob. 5P Ch. 6.7 - Prob. 6P Ch. 6.7 - Prob. 7P Ch. 6.7 - Prob. 8P Ch. 6.7 - Prob. 9P Ch. 6.7 - Prob. 10P Ch. 6.7 - Prob. 11P Ch. 6.7 - Prob. 12P Ch. 6.7 - Prob. 13P Ch. 6.7 - Prob. 14P Ch. 6.7 - Prob. 15P Ch. 6.7 - Prob. 16P Ch. 6.7 - Prob. 17P Ch. 6.7 - Prob. 18P Ch. 6.7 - Prob. 19P Ch. 6.7 - Prob. 20P Ch. 6.7 - Prob. 21P Ch. 6.7 - Prob. 22P Ch. 6.7 - Prob. 23P Ch. 6.7 - Prob. 24P Ch. 6.7 - Prob. 25P Ch. 6.7 - Prob. 26P Ch. 6.7 - Prob. 27P Ch. 6.7 - Prob. 28P Ch. 6.7 - Prob. 29P Ch. 6 - Prob. 1SYU Ch. 6 - Prob. 2SYU Ch. 6 - Prob. 3SYU Ch. 6 - Prob. 4SYU Ch. 6 - Prob. 5SYU Ch. 6 - Prob. 6SYU Ch. 6 - Prob. 7SYU Ch. 6 - Prob. 8SYU Ch. 6 - Prob. 9SYU Ch. 6 - Prob. 10SYU Ch. 6 - Prob. 11SYU Ch. 6 - Prob. 12SYU Ch. 6 - Prob. 13SYU Ch. 6 - Prob. 14SYU Ch. 6 - Prob. 15SYU Ch. 6 - Prob. 16SYU Ch. 6 - Prob. 17SYU Ch. 6 - Prob. 18SYU Ch. 6 - Prob. 19SYU Ch. 6 - Prob. 20SYU Ch. 6 - Prob. 21SYU Ch. 6 - Prob. 22SYU Ch. 6 - Prob. 23SYU Ch. 6 - Prob. 24SYU Ch. 6 - Prob. 25SYU Ch. 6 - Prob. 26SYU Ch. 6 - Prob. 27SYU Ch. 6 - Prob. 28SYU Ch. 6 - Prob. 29SYU Ch. 6 - Prob. 30SYU Ch. 6 - Prob. 31SYU Ch. 6 - Prob. 32SYU Ch. 6 - Prob. 33SYU Ch. 6 - Prob. 34SYU Ch. 6 - Prob. 35SYU Ch. 6 - Prob. 36SYU Ch. 6 - Prob. 37SYU Ch. 6 - Prob. 38SYU Ch. 6 - Prob. 39SYU Ch. 6 - Prob. 40SYU Ch. 6 - Prob. 41SYU Ch. 6 - Prob. 42SYU Ch. 6 - Prob. 43SYU Ch. 6 - Prob. 44SYU Ch. 6 - Prob. 45SYU Ch. 6 - Prob. 46SYU Ch. 6 - Prob. 47SYU Ch. 6 - Prob. 48SYU Ch. 6 - Prob. 49SYU Ch. 6 - Prob. 50SYU Ch. 6 - Prob. 51SYU Ch. 6 - Prob. 52SYU Ch. 6 - Prob. 53SYU Ch. 6 - Prob. 54SYU Ch. 6 - Prob. 55SYU Ch. 6 - Prob. 56SYU Ch. 6 - Prob. 57SYU Ch. 6 - Prob. 58SYU Ch. 6 - Prob. 59SYU Ch. 6 - Prob. 60SYU Ch. 6 - Prob. 61SYU Ch. 6 - Prob. 62SYU Ch. 6 - Prob. 63SYU Ch. 6 - Prob. 64SYU Ch. 6 - Prob. 65SYU Ch. 6 - Prob. 66SYU Ch. 6 - Prob. 67SYU Ch. 6 - Prob. 68SYU Ch. 6 - Prob. 69SYU Ch. 6 - Prob. 70SYU Ch. 6 - Prob. 1FOP Ch. 6 - Prob. 2FOP Ch. 6 - Prob. 3FOP Ch. 6 - Prob. 4FOP Ch. 6 - Prob. 5FOP Ch. 6 - Prob. 6FOP Ch. 6 - Prob. 7FOP Ch. 6 - Prob. 8FOP Ch. 6 - Prob. 9FOP Ch. 6 - Prob. 10FOP Ch. 6 - Prob. 11FOP Ch. 6 - Prob. 12FOP Ch. 6 - Prob. 13FOP Ch. 6 - Prob. 14FOP Ch. 6 - Prob. 15FOP Ch. 6 - Prob. 16FOP Ch. 6 - Prob. 17FOP Ch. 6 - Prob. 18FOP Ch. 6 - Prob. 19FOP Ch. 6 - Prob. 20FOP Ch. 6 - Prob. 21FOP Ch. 6 - Prob. 22FOP Ch. 6 - Prob. 23FOP Ch. 6 - Prob. 24FOP Ch. 6 - Prob. 25FOP Ch. 6 - Prob. 26FOP Ch. 6 - Prob. 27FOP Ch. 6 - Prob. 28FOP Ch. 6 - Prob. 29FOP Ch. 6 - Prob. 30FOP Ch. 6 - Prob. 31FOP Ch. 6 - Prob. 32FOP Ch. 6 - Prob. 33FOP Ch. 6 - Prob. 34FOP Ch. 6 - Prob. 35FOP Ch. 6 - Prob. 36FOP Ch. 6 - Prob. 37FOP Ch. 6 - Prob. 38FOP Ch. 6 - Prob. 39FOP Ch. 6 - Prob. 40FOP Ch. 6 - Prob. 41FOP Ch. 6 - Prob. 42FOP Ch. 6 - Prob. 43FOP Ch. 6 - Prob. 44FOP Ch. 6 - Prob. 45FOP Ch. 6 - Prob. 46FOP Ch. 6 - Prob. 47FOP

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

To evaluate the definite integral using the Fundamental Theorem.

Solution Summary: The author evaluates the definite integral using the Fundamental Theorem.

Concept explainers

Videos

To evaluate the definite integral using the Fundamental Theorem.

Want to see the full answer?

Chapter 6 Solutions