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Asked Dec 2, 2019
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Guess an antiderivative for the integrand function. Validate your guess by differentiation and then evaluate the given definite integral. (Hint: Keep in mind the Chain
Rule in guessing an antiderivative.)
6
dx
0
dx
0
(Type an exact answer in terms of e.)
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Guess an antiderivative for the integrand function. Validate your guess by differentiation and then evaluate the given definite integral. (Hint: Keep in mind the Chain Rule in guessing an antiderivative.) 6 dx 0 dx 0 (Type an exact answer in terms of e.)

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Expert Answer

Step 1

Refer to the question we need to find the antiderivative for the integrand function also validate the guess by differentiation and then evaluate the definite integral.

.xe"dx
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.xe"dx

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Step 2

Now first solve it as indefinite integral as,

1 -fxe"dx
let t x.then dt 2xdx
dt
xdx
2
2
e
+c
2
e
-+c
1(x)
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1 -fxe"dx let t x.then dt 2xdx dt xdx 2 2 e +c 2 e -+c 1(x)

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Step 3

Now differentiate with...

|(x)Ip
dx
d
dx 2
(.*)p
+0
2
=xe
xe
dI
=verified
dx
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|(x)Ip dx d dx 2 (.*)p +0 2 =xe xe dI =verified dx

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Tagged in

Math

Calculus

Integration