Hi I got a few probs with some integration questions such as
Integration by parts:
Limits [0,2] xsinh x dx
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Change of variable rule
Limits [-r,r] (r^2-x^2)^1/2 dx where x =rsint r>0
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and
Limits ["pie"/4, "pie"/2] (dx/sin x) using t = tan x/2)
Any kind of help is well appreciated
Thx
It's a semicircle whose radius is hence its value is
Having this, don't even think to replace the double angle formula for cosine.
First, note that this function is even, so the integral can be rewritten as Besides whose proof is easy, so Let be the value of these integrals, so
and the conclusion follows.
Hi thx for feedback final problem I had was..
Limits [1,10] (1*x^-1/2)*log(x^1/2) dx where x = t^2
First thought that came to mind was the square roots would cancel when substituing t and dt = 1/2*t^3
but the log part left me fogged out only idea I can think of is "(log*x^1/2) ---> 1/t + Constant.
Anything else I could do?