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Evaluate the integral. te⁹t dt Step 1 Recall the formula for integration by parts, which states that if f and g are differentiable functions, then the following holds. [ f(x)g'(x) f(x)g'(x) dx = f(x)g(x) - ) - [ g(x)f'(x) dx If we let u = f(x) and v= g(x), then the differentials are f'(x) dx and dv = g'(x) dx. So, by the Substitution Rule, the formula for integration by parts becomes the following. [udv=uv - [va v du We are given •Stest te⁹t dt. In order to use the formula for integration by parts, we can choose to let u = t and dv= V = Step 2 If u = t and dv=e⁹t dt, then we have the following. du = dt 9t 9t dt.

Evaluate the integral. te⁹t dt Step 1 Recall the formula for integration by parts, which states that if f and g are differentiable functions, then the following holds. [ f(x)g'(x) f(x)g'(x) dx = f(x)g(x) - ) - [ g(x)f'(x) dx If we let u = f(x) and v= g(x), then the differentials are f'(x) dx and dv = g'(x) dx. So, by the Substitution Rule, the formula for integration by parts becomes the following. [udv=uv - [va v du We are given •Stest te⁹t dt. In order to use the formula for integration by parts, we can choose to let u = t and dv= V = Step 2 If u = t and dv=e⁹t dt, then we have the following. du = dt 9t 9t dt.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Evaluate the integral. Step 1 Recall the formula for integration by parts, which states that if f and g are differentiable functions, then the following holds. [F(X) We are given Step 2 te ⁹t dt If we let u= f(x) and v = g(x), then the differentials are f'(x) dx and dv = g'(x) dx. So, by the Substitution Rule, the formula for integration by parts becomes the following. V = f(x)g'(x) dx = f(x)g(x) [udv=uv [te If u = t and dv du = dt ) - [ -Sv du - x)f'(x) dx = e te ⁹t dt. In order to use the formula for integration by parts, we can choose to let u = t and dv = 9t dt, then we have the following. 16° 9t dt.
Transcribed Image Text:Evaluate the integral. Step 1 Recall the formula for integration by parts, which states that if f and g are differentiable functions, then the following holds. [F(X) We are given Step 2 te ⁹t dt If we let u= f(x) and v = g(x), then the differentials are f'(x) dx and dv = g'(x) dx. So, by the Substitution Rule, the formula for integration by parts becomes the following. V = f(x)g'(x) dx = f(x)g(x) [udv=uv [te If u = t and dv du = dt ) - [ -Sv du - x)f'(x) dx = e te ⁹t dt. In order to use the formula for integration by parts, we can choose to let u = t and dv = 9t dt, then we have the following. 16° 9t dt.
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