Complete the table by identifying u and du for the

Travis Fogle

Travis Fogle

Answered question

2021-11-13

Complete the table by identifying u and du for the integral.
f(g(x))g(x)dx u=g(x) du=g(x)dx
(5x2+1)2(10x)dx

Answer & Explanation

Charles Wee

Charles Wee

Beginner2021-11-14Added 14 answers

Let u=g(x) and let g' be continuous over an interval [a,b], and let f be continuous over the range of u=g(x). Then:
abf(g(x))g(x)dx=g(a)g(b)f(u)du
We have:
f(g(x))g(x)dx=(5x2+1)210xdx
Use the formula.
Let it be:
u=g(x)=5x2+1
Now, we differentiate both sides and we have:
du=10xdx
Result: u=5x2+1
du=10xdx

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