 Welcome to the session. Let us discuss the following question. The question says evaluate integral of sine 2x into sine 3x from 0 to pi by 4. Let's now begin with the solution. Let i is equal to integral of sine 2x into sine 3x from 0 to pi by 4. Now we will multiply and divide this integral by 2. So we have 1 by 2 into integral of 2 sine 2x sine 3x from 0 to pi by 4. a minus b minus cos a plus b is equal to 2 sine a sine b. By using this formula we can write 2 sine 2x sine 3x as 0 and upper limit is pi. This is equal to 1 by 2 into integral of cos x minus cos pi pex from 0 to pi to 1 by 2 into integral of cos cos pi pex is sine pi x divided by pi lower limit is 0 and upper limit is pi by 4. The fundamental theorem 2 1 by 2 into sine 5 pi 0 substituted the upper limit and then we have substituted the lower limit. Now this is equal to 1 by 2 into sine pi by