Question

Q7. Evaluate the following. a. \(\int \cos y \ e^y \ dy\) b. \(\int x^2 \sin x \ dx\) c. \(\int \frac{2x - 3}{(x - 2)(x + 5)} \ dx\) d. \(\int \frac{x^2 + 7x + 12}{x + 2} \ dx\) e. \(\int \frac{x^2 + x}{(x^2 + x)(x - 5)} \ dx\) Q8. Solve the following differential equations. a. \((x - 2)dy = (3 - y)dx\) b. \((x + y)dy = (x - y)dx\) c. \(\frac{dy}{dx} = \frac{x^2y}{x^3 + y^3}\) d. \((x^2 - 1)\frac{dy}{dx} + 2xy = \frac{2}{x^2 - 1}\) e. \((1 + x^2)\frac{dy}{dx} + y = \tan^{-1} x\) f. \(e^y(1 - \frac{x}{y})\frac{dy}{dx} + (1 + e^y) = 0\)

          Q7. Evaluate the following.
a. \(\int \cos y \ e^y \ dy\)
b. \(\int x^2 \sin x \ dx\)
c. \(\int \frac{2x - 3}{(x - 2)(x + 5)} \ dx\)
d. \(\int \frac{x^2 + 7x + 12}{x + 2} \ dx\)
e. \(\int \frac{x^2 + x}{(x^2 + x)(x - 5)} \ dx\)
Q8. Solve the following differential equations.
a. \((x - 2)dy = (3 - y)dx\)
b. \((x + y)dy = (x - y)dx\)
c. \(\frac{dy}{dx} = \frac{x^2y}{x^3 + y^3}\)
d. \((x^2 - 1)\frac{dy}{dx} + 2xy = \frac{2}{x^2 - 1}\)
e. \((1 + x^2)\frac{dy}{dx} + y = \tan^{-1} x\)
f. \(e^y(1 - \frac{x}{y})\frac{dy}{dx} + (1 + e^y) = 0\)

Q7. Evaluate the following.
a. ∫cos y e^y dy
b. ∫ x^2 sin x dx
c. ∫(2x - 3)/((x - 2)(x + 5)) dx
d. ∫(x^2 + 7x + 12)/(x + 2) dx
e. ∫(x^2 + x)/((x^2 + x)(x - 5)) dx
Q8. Solve the following differential equations.
a. (x - 2)dy = (3 - y)dx
b. (x + y)dy = (x - y)dx
c. (dy)/(dx) = (x^2y)/(x^3 + y^3)
d. (x^2 - 1)(dy)/(dx) + 2xy = (2)/(x^2 - 1)
e. (1 + x^2)(dy)/(dx) + y = tan^-1 x
f. e^y(1 - (x)/(y))(dy)/(dx) + (1 + e^y) = 0

Added by Sherry M.

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