Question

can someone help me solve... this integral... im going to post it

Answer 1

first apply formula for integratng .
put limits.
differentiate

Answer 2

What is the derivative of
\[
\int_0^x \frac {dt}{1+t^2}
\]

Answer 3

What is the derivative of
\[\int_0^{x^5} \frac {dt}{1+t^2}

\]

Answer 4

hint:by definition of a definite integration\[\int_{a(x)}^{b(x)}f(t)dt=F(b(x))-F(a(x))\]and by deriving and the chain rule
\[\frac{d}{dx}[F(b(x))-F(a(x))]=f(b)b'-f(a)a'\]

Answer 5

You can replace 0 by any number a in my questions above.