- #1

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**1. If g(x) = ∫ f(t) dt = xln x, find f(1)**

The ∫ has x^2 on top and 0 on bottom.

The ∫ has x^2 on top and 0 on bottom.

**2.**g'(x) = f(x) <--FTC1

## The Attempt at a Solution

g'(x) = f(x) u=x^2

g'(x) = u*lnu * 2x(derivative of inner function)

g'(x) = 2x(x^2)ln(x^2)

f(1) = 2(1)(1^2)ln(1^2)

f(1) = 0, since ln(1) = 0

I keep getting 0, and I'm not sure how 0 is not the answer... The answer key says the solution is 1/2. I really don't know what I'm doing wrong :(