1. Compute the right hand sum R4 for g(x): = cos (πx) on [0, 1].
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![1. Compute the right hand sum R4 for g(x)= = cos (Tx) on [0, 1].
2. Estimate the integral f 1 dx by using two approximating rectangles
and mid-points. Round your answer to three decimal places.
3. Evaluate the integral
(3-x) dx using area formulas.
4. Use the Fundamental Theorem of Calculus, Part 1, to find the deriva-
tivet dt.
rsin
5. Find the derivative of the function g(x) = findt.
6. Use basic integration formulas to compute the definite integral,
* (sin x - cos x) dx
7. Find an antiderivative of the function f(x) = (x - 1) (2x + 3)
8. Find the most general antiderivative of the function f(x) = ²+x+x³/²
x
9. Find the antiderivative using the indicated substitution.
[(x − 1)(x² − 2x)³ dx; u = x² – 2x
10. Find the indefinite integral
11. Find the integral
de
12. The velocity in meters per second of a particle moving along a line is
v(t) = -2t+4, 0≤ t ≤ 3. Write an expression to represent the total
distance traveled in meters by the particle in the given time interval.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F41ac0bc6-a1c1-4386-be1d-f7047d2be053%2Fcf07cc4e-d2e2-4e94-9386-546d0623308b%2Fso49947_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Compute the right hand sum R4 for g(x)= = cos (Tx) on [0, 1].
2. Estimate the integral f 1 dx by using two approximating rectangles
and mid-points. Round your answer to three decimal places.
3. Evaluate the integral
(3-x) dx using area formulas.
4. Use the Fundamental Theorem of Calculus, Part 1, to find the deriva-
tivet dt.
rsin
5. Find the derivative of the function g(x) = findt.
6. Use basic integration formulas to compute the definite integral,
* (sin x - cos x) dx
7. Find an antiderivative of the function f(x) = (x - 1) (2x + 3)
8. Find the most general antiderivative of the function f(x) = ²+x+x³/²
x
9. Find the antiderivative using the indicated substitution.
[(x − 1)(x² − 2x)³ dx; u = x² – 2x
10. Find the indefinite integral
11. Find the integral
de
12. The velocity in meters per second of a particle moving along a line is
v(t) = -2t+4, 0≤ t ≤ 3. Write an expression to represent the total
distance traveled in meters by the particle in the given time interval.
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