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13. (a) Find g(1) so that fg() dt =4- +2-sin". (b) Evaluate g(t) dt using the Evaluation Theorem. (c) Evaluate g(t) dt by the area interpretation of the integral. Compare your answer with part (b) above. (d) Evaluate g(t) dt.

13. (a) Find g(1) so that fg() dt =4- +2-sin". (b) Evaluate g(t) dt using the Evaluation Theorem. (c) Evaluate g(t) dt by the area interpretation of the integral. Compare your answer with part (b) above. (d) Evaluate g(t) dt.

Advanced Engineering Mathematics
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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Here is the transcribed text from the image, suitable for an educational website: --- ### Integral Calculus Problems **13.** (a) Find \( g(t) \) so that \[ \int g(t) \, dt = \frac{t}{2} \sqrt{4 - t^2} + 2 \cdot \sin^{-1} \frac{t}{2} \] (b) Evaluate \[ \int_{0}^{2} g(t) \, dt \] using the Evaluation Theorem. (c) Evaluate \[ \int_{0}^{2} g(t) \, dt \] by the area interpretation of the integral. Compare your answer with part (b) above. (d) Evaluate \[ \int_{0}^{\sqrt{3}} g(t) \, dt \] **14.** \( v(t) \) is the velocity of a moving object measured in feet per minute. --- This section focuses on practicing the evaluation of definite integrals and understanding their geometric interpretations.
Transcribed Image Text:Here is the transcribed text from the image, suitable for an educational website: --- ### Integral Calculus Problems **13.** (a) Find \( g(t) \) so that \[ \int g(t) \, dt = \frac{t}{2} \sqrt{4 - t^2} + 2 \cdot \sin^{-1} \frac{t}{2} \] (b) Evaluate \[ \int_{0}^{2} g(t) \, dt \] using the Evaluation Theorem. (c) Evaluate \[ \int_{0}^{2} g(t) \, dt \] by the area interpretation of the integral. Compare your answer with part (b) above. (d) Evaluate \[ \int_{0}^{\sqrt{3}} g(t) \, dt \] **14.** \( v(t) \) is the velocity of a moving object measured in feet per minute. --- This section focuses on practicing the evaluation of definite integrals and understanding their geometric interpretations.
Expert Solution
Step 1

a) To find g(t) so that ∫g(t)dt=t24-t2+2sin-1t2

Using the fundamental theorem of calculus,

g(t)=ddtt24-t2+2sin-1t2

Solving this step by step,

Using (f+g)'=f'+g'

g(t)=ddtt24-t2+ddt2sin-1t2................................(1)

 

 

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