Page:Calculus Made Easy.pdf/225

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

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

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