91.

$\int \frac{\mathrm{dx}}{{\mathrm{a}}^2{\sin }^2\left(\mathrm{x}\right) + {\mathrm{b}}^2{\cos }^2\left(\mathrm{x}\right)}$ is equal to

• $\frac{1}{\mathrm{ab}}{\tan }^{-1}\left(\frac{\mathrm{atan}\left(\mathrm{x}\right)}{\mathrm{b}}\right) + \mathrm{C}$

• ${\tan }^{-1}\left(\frac{\mathrm{atan}\left(\mathrm{x}\right)}{\mathrm{b}}\right) + \mathrm{C}$

• $\frac{1}{\mathrm{ab}}{\tan }^{-1}\left(\frac{\mathrm{btan}\left(\mathrm{x}\right)}{\mathrm{a}}\right) + \mathrm{C}$

• ${\tan }^{-1}\left(\frac{\mathrm{btan}\left(\mathrm{x}\right)}{\mathrm{a}}\right) + \mathrm{C}$

${\int }_0^{\raisebox{1ex}{$\mathrm{\pi }$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}{\sin }^8\left(\mathrm{x}\right){\cos }^2\left(\mathrm{x}\right)\mathrm{dx}$ is equal to

• $\frac{\mathrm{\pi }}{512}$

• $\frac{3\mathrm{\pi }}{512}$

• $\frac{5\mathrm{\pi }}{512}$

• $\frac{7\mathrm{\pi }}{512}$

${\int }_{- 1}^1\left({\mathrm{ax}}^3 + \mathrm{bx}\right)\mathrm{dx} = 0$ for

• any value of a and b

• a > 0, b > 0 only

• a > 0, b > 0 only

• a < 0, b > 0 only

Using the Trapezoidal rule, the approximate value of ${\int }_1^4\mathrm{ydx}$

• 0.1833

• 1.1833

• 2.1833

• 3.1833

The solution of xdx + ydy = x²ydy - xy²dx is

• x² - 1 = C(1 + y²)

• x² + 1 = C(1 - y²)

• x² - 1 = C(1 - y²)

• x² + 1 = C(1 - y²)

The solution of x² + y²$\frac{\mathrm{dy}}{\mathrm{dx}}$ = 4 is

• x² + y² = 12x + C

• x² + y² = 3x + C

• x² + y² = 8x + C

• x³ + y³ = 12x + C

The solution of $\frac{\mathrm{dy}}{\mathrm{dx}} + \mathrm{y} = {\mathrm{e}}^{\mathrm{x}}$ is

• 2y = e^2x + C

• 2ye^x = e^x + C

• 2ye^x = e^2x + C

• 2ye^2x = 2e^x + C

If y = $\mathrm{y} = \mathrm{Acos}\left(\mathrm{nx}\right) + \mathrm{Bsin}\left(\mathrm{nx}\right)$, then y₂ + n²y is equal to

• 0

• 1

• y

• - 1

$\mathrm{If} \mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D} \mathrm{are} \mathrm{angles} \mathrm{of} \mathrm{a} \mathrm{cyclic} \mathrm{quadrilateral},\mathrm{then}$$\cos \left(\mathrm{A} \right)+ \cos \left(\mathrm{B} \right)+ \cos \left(\mathrm{C}\right) + \cos \left(\mathrm{D}\right)$ is equal to

• 0

• 1

• - 1

• 4

$\mathrm{The} \mathrm{equation} \sqrt{3}\mathrm{sinx} + \mathrm{cosx} =4,\mathrm{has}$

• only one solution

• two solution

• infinitely many solution

• No solution