Question

∫²(x^3 cos x/2+ 1/2)√4-x^2 dx

solve by graphical method

Answer 1

We first define I = ∫ex sin(2x) dx, v = sin(2x) and du/dx = ex and use integration by parts as follows

I = ∫ex sin(2x) dx

= [ex sin(2x)] - ∫ex 2 cos(2x) dx

We now let V = ex and du/dx = ex and use the integration by parts one more time

= [ex sin(2x)] - 2[ex cos(2x)] + 2 ∫ ex 2 (- sin(2x)) dx

= [ex sin(2x)] - 2[ex cos(2x)] - 4∫ex sin(2x) dx

We can write the integral I as follows

I = [ex sin(2x)] - 2[ex cos(2x)] - 4I

Answer 2

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