00:01
Hi, there is a question in this i need to solve 1 to 4 x square e raised to the power 2x dx by using integration by parts.
00:14
So i'll be using the formula that if i have to integrate u into v dx where u and v are the functions of x, then if i take u as first function v as second function, it becomes first function integration of second function minus differentiation of first function integration of second function and whole integration.
00:45
Now this function u and v are selected by or the function 1 and 2 are selected by the rule known as euler's rule where i is inverse trigonometric function, l is linear logarithmic function, a is algebraic function, t is trigonometric function and e is exponential function.
01:04
Now here this is exponential function.
01:06
So this cannot be taken as first function.
01:08
This will be second function.
01:09
This is first, this is second.
01:12
Now let us start solving that from 1 to 4.
01:18
So first function integration of second function minus differentiation of first function integration of second function and whole integration x square e raised to the power 2x divided by 2 integration of e raised to the power 2x is e raised to the power 2x by 2 minus integration of its differentiation is 2x and again e raised to the power 2x by 2 and dx and one thing to be noted that we have 1 to 4 as limits 1 to 4.
02:07
Is that correct? 1 to 4 yeah...