Question

Consider the integral ∫x^4 (x^5-10)^6 dx. To find the value of this integral, make the substitution u=x^5 - 10. a) Write (x^5-10)^6 in terms of u: b) This makes x^4 dx = c) Re-write the integral in terms of u and du, and find the antiderivative. The antiderivative in terms of u is: d) Now back-substitute and write your answer to part (c) in terms of x:

Name: 1 consider the integral x4 x5 106 dx to find the value of this integral make the substitution ux5 10 a write x5106x5 106 in terms of u b this makes x4 dx c re write the integral in terms of 56635
Uploaded: 2022-06-29T06:53:52-08:00
Duration: 4 min 11 s
Channel: Suman K
Description: 1 consider the integral x4 x5 106 dx to find the value of this integral make the substitution ux5 10 a write x5106x5 106 in terms of u b this makes x4 dx c re write the integral in terms of 56635

          Consider the integral ∫x^4 (x^5-10)^6 dx.
To find the value of this integral, make the
substitution u=x^5 - 10.
a) Write (x^5-10)^6 in terms of u: 
b) This makes x^4 dx = 
c) Re-write the integral in terms of u and du, and
find the antiderivative.
The antiderivative in terms
of u is:    
d) Now back-substitute and write your answer to part (c) in terms
of x:

Added by Felipe L.

Calculus: Early Transcendentals

James Stewart 8th Edition

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Solved by Expert Suman K

06/29/2022

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Consider the integral ∫x^4 (x^5-10)^6 dx. To find the value of this integral, make the substitution u=x^5 - 10. a) Write (x^5-10)^6 in terms of u: b) This makes x^4 dx = c) Re-write the integral in terms of u and du, and find the antiderivative. The antiderivative in terms of u is: d) Now back-substitute and write your answer to part (c) in terms of x: