Thread: Definite integration help.

My logic may be horrible.

Differentiate g(x)= definite integral on [2, x^2+3x-1] sec(t)dt and then prove the theorem you applied.

= antiderivative of sec(x^2+3x-1) - antiderivative of sec(2)

d/dx(ntiderivative of sec(x^2+3x-1) - antiderivative of sec(2))

= sec(x^2+3x-1) - sec(2)

Which is exactly what the integral originally states, isn't it?

Originally Posted by pantsaregood

My logic may be horrible.

Differentiate g(x)= definite integral on [2, x^2+3x-1] sec(t)dt and then prove the theorem you applied.

= antiderivative of sec(x^2+3x-1) - antiderivative of sec(2)

d/dx(ntiderivative of sec(x^2+3x-1) - antiderivative of sec(2))

= sec(x^2+3x-1) - sec(2)

Which is exactly what the integral originally states, isn't it?

If I understand this correctly we have



This can be viewed as a function composition. Let

Then

Now by the chain rule



Remember that the fundemental theorem of calculus says that(Notice the upper limit of integration) check you book for the hypothsis



Combining these two results we get



Notice that if you integrate both sides of the last equaion with the same u substition that we did above you will get the same function g back. i.e

I hope this helps