I need help with answer Evaluate the integral.+ 6)eX dx3.95

Given: I=∫01x2+6e-xdx ...(1) The expression for the integration by parts: ∫udv=u·v-∫vdu Now apply…

Answered: Evaluate the integral. + 6)e-x 3.95

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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Step 1

Given:

$I = \int_{0}^{1} (x^{2} + 6) e^{- x} d x$ ...(1)

The expression for the integration by parts:

$\int u d v = u \cdot v - \int v d u$

Now apply the integration by parts to solve the above integral.

Let,

$\begin{array}{rcl} u & = & x^{2} + 6; d v = e^{- x} d x \\ \frac{d u}{d x} & = & \frac{d}{d x} (x^{2} + 6); \int d v = \int e^{- x} d x \\ \frac{d u}{d x} & = & 2 x + 0; v = - e^{- x} \\ d u & = & 2 x d x; v = - e^{- x} \end{array}$

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