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Evaluate ∫ dx ) 1- x( 2 (a) x 5 /5 – 2/3 x 3 + x + k (b) kx 3 x 3 +− (c) 2x (d) none of these 5. ∫ + ) x 1 ( ) 3x –1 ( dx is equal to (a) x – x 2 – x 3 (b) x 3 – x 2 + x (c) x – x 2 – x 3 + k (d) none of these 6. [ ] ∫ x/1–x dx is equal to (a) 3 2 x 3/2 – 2 x ½ +k (b) kx2x 3 2 +− (c) k xx2 1 x2 1 ++ (d) none of these 7. The integral of px 3 + qx 2 + rk + w/x is equal to (a) px 2 + qx + r + k (b) px 3 /3 + qx 2 /2 + rx (c) 3px + 2q – w/x 2 (d) none of these 8. Use method of substitution to integrate the function f(x) = ( 4x + 5 ) 6 and the answer is (a) 1/28 ( 4x + 5 ) 7 + k (b) ( 4x + 5 ) 7 /7 + k (c) ( 4x + 5 ) 7 9. Use method of substitution to evaluate ∫ + 52 )4x(x dx and the answer is 10. Integrate ( x + a ) n and the result will be
Q. State and prove fundamental theorem of integral calculus.
Find the area of the region that lies inside the first curve and outside the second curve. r2 = 18 cos 2θ, r = 3
Find the reduction formula of ʃsec6xdx.
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