00:02
Hi, in this question, we have been given integration of t times e raised to the power minus 2t dt and we need to find the integration of this.
00:14
So here we will use product rule of integration, that is integration of u times v is equal to, we will take u constant and we will integrate v then minus integration of whatever we had kept the function constant, we will differentiate this then multiplied by integration of the other function and then whole will be integrated.
00:36
So we will be using this formula, so we can write i is equal to, here we will consider t as u and e raised to the power minus 2t as v.
00:45
So this will be t times integration of e raised to the power minus 2t dt minus integration of derivative of t multiplied by integration of e raised to the power minus 2t dt and whole will be then integrated.
01:04
Since we know that integration of e raised to the power ax dx is equal to e raised to the power ax divided by a plus constant of integration.
01:16
So this i will be equal to t times e raised to the power minus 2t divided by minus 2 then minus integration of, so the derivative of t with respect to t is 1 and again here we have e raised to the power minus 2t divided by minus 2 and this is dt...