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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Using Integration Tables In Exercises 37– 44, use the integration table in Appendix C to evaluate the definite integral. See Example 4.

0 5 x 5 + 2 x d x

To determine

To calculate: The solution of definite integral 05x5+2xdx.

Explanation

Given Information:

The provided definite integral is;

05x5+2xdx

Formula used:

The formula for the integral ua+budu is;

ua+budu=2(2abu)3b2a+bu+C

The General power differentiation Rule:

ddx[un]=nun1dudx

Calculation:

Consider u=x.

Differentiate the considered function with respect to x using power rule of differentiation.

du=dx

Consider the provided expression:

05x5+2xdx

Here, a=5, b=2, u=x and du=dx.

Substitute u for x, a for 5, b for 2, and du for dx;

05x5+2xdx=05ua+budu

Now, Use the above integration formula and solve the above integral as;

05x5+2xdx=[2(2abu)3b2a+bu]05

Substitute x for u, 5 for a, and 2 for b

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