Page:Calculus Made Easy.pdf/225

Exercises XVII. (See p. 263 for the Answers.)

(1) Find $\int y\,dx$ when $y^{2}=4ax$.

(2) Find $\int {\frac {3}{x^{4}}}\,dx$.

(3) Find $\int {\frac {1}{a}}x^{3}\,dx$.

(4) Find $\int (x^{2}+a)\,dx$.

(5) Find $5x^{-{\frac {7}{2}}}$.

(6) Find $\int (4x^{3}+3x^{2}+2x+1)\,dx$.

(7) Find ${\dfrac {dy}{dx}}={\dfrac {ax}{2}}+{\dfrac {bx^{2}}{3}}+{\dfrac {cx^{3}}{4}}$; find $y$.

(8) Find $\int \left({\frac {x^{2}+a}{x+a}}\right)dx$.

(9) Find $\int (x+3)^{3}\,dx$.

(10) Find $\int (x+2)(x-a)\,dx$.

(11) Find $\int ({\sqrt {x}}+{\sqrt[{3}]{x}})3a^{2}\,dx$.

(12) Find $\int (\sin \theta -{\tfrac {1}{2}})\,{\frac {d\theta }{3}}$.

(13) Find $\int \cos ^{2}a\theta \,d\theta$.

(14) Find $\int \sin ^{2}\theta \,d\theta$.

(15) Find $\int \sin ^{2}a\theta \,d\theta$.

(16) Find $\int \epsilon ^{3x}\,dx$.

(17) Find $\int {\dfrac {dx}{1+x}}$.

(18) Find $\int {\dfrac {dx}{1-x}}$.