Explanation Given Information: The function is ∫ ( x + 1 ) [ cos ( x 2 + 2 x ) + ( x 2 + 2 x ) ] d x . Formula Used: The following integration formula is used: ∫ cos x d x = sin x + C The derivation formula, d d x a = 0 , where a is all-natural numbers. And, d d x x n = n x n − 1 Calculation: Consider the provided function ∫ ( x + 1 ) [ cos ( x 2 + 2 x ) + ( x 2 + 2 x ) ] d x . Replace the parenthetical expression with variable u . u = x 2 + 2 x Determine the derivative of u with respect to x. d u d x = d d x ( x 2 + 2 x ) = d d x x 2 + d d x ( 2 x ) = 2 x 2 − 1 + 2 = 2 x + 2 Determine the value of d x . d x = 1 2 x + 2 d u Substitute the value of d x into the integral. ∫ ( x + 1 ) [ cos ( x 2 + 2 x ) + ( x 2 + 2 x ) ] d x = ∫ ( x + 1 ) ( cos ( u ) + u ) ⋅ ( 1 2 x + 2 ) d u Further solve as, ∫ ( x + 1

Student Solutions Manual for Waner/Costenoble's Finite Math and Applied Calculus, 7th

7th Edition

ISBN: 9781337275972

Author: Waner, Stefan; Costenoble, Steven

Publisher: Cengage Learning

See similar textbooks

Videos

Question

Chapter 16.3, Problem 12E

To determine

To calculate: The solution of the integral function ∫(x+1)[cos(x2+2x)+(x2+2x)]dx.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 16.3, Problem 11E

Chapter 16.3, Problem 13E

Students have asked these similar questions

3. Consider the sequences of functions f₁: [-π, π] → R, sin(n²x) An(2) n f pointwise as (i) Find a function ƒ : [-T,π] → R such that fn n∞. Further, show that fn →f uniformly on [-π,π] as n → ∞. [20 Marks] (ii) Does the sequence of derivatives f(x) has a pointwise limit on [-7, 7]? Justify your answer. [10 Marks]

1. (i) Give the definition of a metric on a set X. [5 Marks] (ii) Let X = {a, b, c} and let a function d : XxX → [0, ∞) be defined as d(a, a) = d(b,b) = d(c, c) 0, d(a, c) = d(c, a) 1, d(a, b) = d(b, a) = 4, d(b, c) = d(c,b) = 2. Decide whether d is a metric on X. Justify your answer. = (iii) Consider a metric space (R, d.), where = [10 Marks] 0 if x = y, d* (x, y) 5 if xy. In the metric space (R, d*), describe: (a) open ball B2(0) of radius 2 centred at 0; (b) closed ball B5(0) of radius 5 centred at 0; (c) sphere S10 (0) of radius 10 centred at 0. [5 Marks] [5 Marks] [5 Marks]

(c) sphere S10 (0) of radius 10 centred at 0. [5 Marks] 2. Let C([a, b]) be the metric space of continuous functions on the interval [a, b] with the metric doo (f,g) = max f(x)g(x)|. xЄ[a,b] = 1x. Find: Let f(x) = 1 - x² and g(x): (i) do(f, g) in C'([0, 1]); (ii) do(f,g) in C([−1, 1]). [20 Marks] [20 Marks]

Chapter 16 Solutions

Student Solutions Manual for Waner/Costenoble's Finite Math and Applied Calculus, 7th

Ch. 16.1 - Prob. 1E Ch. 16.1 - Prob. 2E Ch. 16.1 - Prob. 3E Ch. 16.1 - Prob. 4E Ch. 16.1 - Prob. 5E Ch. 16.1 - Prob. 6E Ch. 16.1 - Prob. 7E Ch. 16.1 - Prob. 8E Ch. 16.1 - Prob. 9E Ch. 16.1 - Prob. 10E

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.

The solution of the integral function ∫ ( x + 1 ) [ cos ( x 2 + 2 x ) + ( x 2 + 2 x ) ] d x .

Solution Summary: The author explains how to calculate the integral function displaystyle

Videos

To calculate: The solution of the integral function ∫(x+1)[cos(x2+2x)+(x2+2x)]dx.

Want to see the full answer?

Chapter 16 Solutions