integration

Like I understand both curves intersect at x as they are the inverse and its way too hard to find the inverse but using x instead of the inverse wont give u the correct shaded area

does anyone know how to do this ? I tried doing it and i got it wrong

I got part a ) For b) I managed to prove k^k < 1/4(k+1)^k+1 but i am struggling to prove the middle bit for some reason which shouldnt be that hard but idk why im struggling lol

I came across an integral that my teacher gave me to do. I have an answer but am unsure if my answer is correct. Other softwares (wolfram alpha and symbolab) are giving me different answers, but I suspect they are algebraically equivalent since they probably have different constants of...

I am up to the last question in the exercise and I am a bit stuck on this question: Can anyone please help me out on this ?

I am pretty confused with my solution to this integration proof question. I feel like it isn't the right way to prove it. d/dx (uv) = u(dv/dx)+v(du/dx) take the integral with respect to x of both sides: uv = ∫ u(dv/dx ) dx + ∫ v(du/dx) dx therefore, ∫ u(dv/dx ) dx = uv - ∫ v(du/dx)...

Hi, I am doing 4u maths, so advanced maths it not going to be assessed for me. However, I am new to integration so I started doing 2u integration from the Cambridge Maths book, however the questions are very similar and not that challenging. So if anyone has any harder worksheets for 2u...

What are all the types of integration by parts questions? I know normal IBP, and the other type where you have to integrate 2 times, and a 3rd type where you have to integrate 2 times and then move a repeated integral from RHS to LHS and then divide by 2. Are there any more trick question...

I am struggling to do this question. I tried solving it and yeah thats pretty much it. I tried :(. Also generally, I can do integration by parts questions very well but whenever it comes to reduction formula or proof by Induction questions where there is a recursive formula involved, I only get...