Question

calculus ..help .......pl

Answer 1

There are multiple ways of doing this question

Answer 2

\[\int\limits_{0}^{2a}t ^{3}\sqrt{2at-t ^{2}}dt\]
Let's apply a exponential property to get rid of the sqrt.
\[\int\limits\limits_{0}^{2a}t ^{3}(2at-t ^{2})^{\frac{ 1 }{ 2 }}dt\]

Answer 3

i know there e many ways ... but i am stuck .. soo help pll ..@Owlcoffee i did not get u ..

Answer 4

@Owlcoffee got u watshould we take for t

Answer 5

One popular way is to assume t = some trigonometric function that simplifies the expression inside the square root

Answer 6

True, but it's better if we use some simple factorization, and then evaluate.
Do we have to find "a" by any chance?

Answer 7

no we just have to integrate ....

Answer 8

@Owlcoffee ????????????/

Answer 9

@amistre64

Answer 10

\(t = 2a \sin^2 x\)

Answer 11

i believe Hartnn applied the integration by parts formula, it's a good way to solve the integral if the product of two functions.

Answer 12

@hartnn : you should have let her find the function :)

Answer 13

use this formula:
\[\int\limits_{}^{}u.v \prime dx = u.v-\int\limits_{}^{}u \prime.v dx\]

Answer 14

thanku ... i know the formulae.... .. will try ..

Answer 15

wat will be the limits ., ????? no it 0 to 2a ... after substitituon ..... i know its simple ..but i always get confuse .. soo .... ??/

Answer 16

@shkrina: Use t = 2a sin^2 x as @hartnn suggested.....u will get the answer more easily

Answer 17

k