# Thread: ratio of two definite Integration

1. ## ratio of two definite Integration

$If I = \int^{1}_{0}x^{\frac{5}{2}}(1-x)^{\frac{7}{2}}dx and J = \int^{1}_{0}\frac{x^{\frac{3}{2}}(1-x)^{\frac{7}{2}}}{(3+x)^8}dx . Then \displaystyle \frac{I}{J} is$

2. ## Re: ratio of two definite Integration

I think I know how to do this although my answer is pretty disgusting (could be wrong). I don't know how to use latex so I'll just tell you what I did.

So since the integrals have the same limits and variable, if you write the integral of I/J, its the same as finding the values of I and J and then dividing it. When you re-write the integral the (1-x)^7/2 terms cancel out and the x^5/2 is just reduced to x. So you're left with x(3+x)^8. Then it's just a sub for 3+x and bob's your uncle.

3. ## Re: ratio of two definite Integration

$\left(\int_a^b f(x)\, dx\right)/ \left(\int_a^b g(x)\, dx\right)\neq \int_a^b \frac{f(x)}{g(x)}\, dx$
in general.

Eg let a=0, f(x)=x^2, g(x)=x.

4. ## Re: ratio of two definite Integration

Oh. Man I just tried to type up my solution in LaTex for the 1st time but I didn't know how to put it as text in the document only as a picture. How do I put it as text like the posts above (even though ik it's wrong now -_- )

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