Indefinite Integral Practice Name: 1. Verify the statement by showing that the derivative of the right side is equal to the integrand of the left side. a. 4 3 9 3 dx C x x ⎛ ⎞ − = + ⎜ ⎟ ⎝ ⎠ ∫ b. 3 2 3 1 1 3 dx x x C x ⎛ ⎞ − = − + ⎜ ⎟ ⎝ ⎠ ∫ 2. Integrate. a. 6dx ∫ b. 2 3 t dt ∫ c. 3 5 x dx − ∫ d. du ∫ e. 3 2 x dx ∫ f. 3 xdx ∫ g. 1 dx x x ∫ h. 3 1 2 dx x ∫ i. ( ) 3 2 x dx + ∫ j. ( ) 4 3 2 3 1 x x dx + − ∫ k. 2 3 x dx ∫ l. 3 1 dx x ∫ m. 2 1 4 dx x ∫ n. 2 2 2 t dt t + ∫ o. ( ) 2 3 1 u u du + ∫ p. ( )( ) 1 6 5 x x dx − − ∫ q. 2 y ydy ∫ 3. Given below are the derivative graph, f x () , find a possible equation for Fx () the antiderivative of f x () a. b. Answers: (Of course, you could have checked all of yours using differentiation!) 2. a. 6 x C + b. 3 t C + c. 2 5 2 C x − + d. u C + e. 5 2 2 5 x C + f. 4 3 3 4 x C + g. 2 C x − + h. 2 1 4 C x − + i. 4 2 4 x x C + + j. 7 2 3 6 3 7 2 x x x C + − + k. 5 3 3 5 x C + l. 2 1 2 C x − + m. 1 4 C x − + n. 2 t C t − + o. 4 2 3 1 4 2 u u C + + p. 3 2 11 2 5 2 x x x C − + + q. 7 2 2 7 y C + 3. Example solution a. Fx () = 2 x + 3 b. Fx () = 1 2 x 2 + 5