1. Choose the correct answer from the bracket.∫ex dx = -(e2x + c,

1.	1. Choose the correct answer from the bracket.∫ex dx = -(e2x + c, e-x + c, e2x + c) 2. Evaluate: ∫ ex sinxdx
Answer» 1. e^x + c 2. I = ∫e^x sinxdx = sinx.e^x – ∫cos x.e^xdx = sin x.e^x – (cos x.e^x – ∫(- sin x).e^x dx) = sinx.e^x – cosxe^x – ∫sinx.e^xdx = sin x.e^x – cos xe^x – I 2I = sin x.e^x – cos xe^x I = \(\frac{1}{2}\)e^x(sinx – cosx) + c.

1. Choose the correct answer from the bracket.∫ex dx = -(e2x + c, e-x + c, e2x + c) 2. Evaluate: ∫ ex sinxdx

Answer»

1. e^x + c

2. I = ∫e^x sinxdx = sinx.e^x – ∫cos x.e^xdx

= sin x.e^x – (cos x.e^x – ∫(- sin x).e^x dx)

= sinx.e^x – cosxe^x – ∫sinx.e^xdx

= sin x.e^x – cos xe^x – I

2I = sin x.e^x – cos xe^x

I = \(\frac{1}{2}\)e^x(sinx – cosx) + c.