4 0 1 2  4 l Example 3 2 t 1  sin x dx 4 Solution Cos x is the derivative of 1 + sin x du Put u = I + sin x, dx  cos x du = cos x dx 2 2 cos x du  dx 0 0 1  sin x u = ln u (For definite integral we need not put the constant of integration) ln 1 ln 1   67 ln  2 (0 )  = ln 2 Example 4 2 x 3 e Evaluate 0 dx Solution 2 x 3 3 0 6 2 2 1 2
1 4 2 0  4 Example 3 2 1  sin x dx 4 Solution Cos x is the derivative of 1 + sin x Put u = I + sin x, du dx  cos x du = cos x dx 2 0 cos x 1  sin x dx  2 0 du u = ln u (For definite integral we need not put the constant of integration)  ln 1  ln 1 67  ln 2  (0 ) = ln 2 Example 4 Evaluate 3 e 0 2 x dx Solution 3 2 x 3 0 6 2 2 1 2 l t
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