Help Me With This Integral Problems?

Question

Can someone explain to me how to find:

d/dx of the integral from 0.5 to x arctan(t^2) dt

Answer 1

It's just arctan (x^2).

By the fundamental theorem of calculus, if F(t) is the antiderivative of f(t) = arctan(t^2), then the integral of f(t) from 0.5 to x will give F(x) - F(0.5). The derivative of this function with respect to x then gives you f(x).

Answer 2

let f(x) = acrctan(t^2)
let F(x) be the antiderivitive of f(x)
then

t = x
⌠ f(x) = [F(x)] from t = 0.5 to t = x
⌡
t = 0.5

which equals F(x) - F(0.5)

But you want the derivitive of this

d F(x)/dx = f(x)
because f(x) is the derivitive of F(x) and the derivitive of a constant F(0.5) is 0.

and f(x) = acrctan(x^2)
which is your answer.

Answer 3

u need an explanation it is 534e356^yuutioo8-uuunarctan6432 dats ur correct answer ur teacher will mark it 4 u dont woory are u okay

Answer 4

go here...

http://www.math.ubc.ca/~sjer/math101sec201/Review/ftc.pdf