calculus1 integral

[calculus151]

i've solves a but i couldn't solved b
can anyone help me

 

[Deleted member 4993]

i've solves a but i couldn't solved b
can anyone help me
View attachment 30486

Do you know Liebniz's theorem? If yes - apply it.

If not - Google the term and come back if you do not understand something.

 

[pka]

For part b): if each of [imath]\alpha(x)~\&~\beta(x)[/imath] is a differentiable function then if
[imath]\displaystyle G(x) = \int_{\beta (x)}^{\alpha (x)} {\Phi (t)dt}[/imath] we get [imath]G^{\prime}(x)=\alpha^{\prime}(x)\Phi(\alpha(x))-\beta^{\prime}(x)\Phi(\beta(x))[/imath]