Thread: Integration

there are 3 some questions from my Calculus homework that are giving me real head ache ! , please help dudes

have to get the integral of the followings
1. dx / ( 2e^x ) * sqr root ( 1 - e^2x ) INDEFINITE

2. { sqr root [ (1 - x^2)^3 ] } dx [0,1] DEFINITE

3. { x^3 * sin^2 * x / x^4 + 2x^2 + 1 } dx [-5,5] DEFINITE


please write the way of how to do each question with formulas used, it would be very very nice of you ! thanks alot in advanced !

Hello & a very warm Welcome to the forum

Originally Posted by masterjoint

1. dx / ( 2e^x ) * sqr root ( 1 - e^2x )

put

so

hence


so



put

so


hence


put

so


I am too lazy to continue so go ahead if unsolved feel free to ask

The second one is difficult to integrate by elementary methods. But, I do not think it is required. It is a matter of observation to note we have an odd function. Since we integrate from -5 to 5, it evaluates to 0.