1. Tardigrade
  2. Question
  3. Mathematics
  4. ∫ (3 sin x-2 cos x/4 cos x+5 sin x) d x=

Q. $\int \frac{3 \sin x-2 \cos x}{4 \cos x+5 \sin x} d x=$

KCETKCET 2022 Report Error

Solution:

$\int \frac{a \cos x+b \sin x}{c \cos x+d \sin x}=\frac{a c+b d}{c^{2}+d^{2}} x+\frac{a d-b c}{c^{2}+d^{2}} \log (c \cos x+d \sin x) $ (Short cut)
Required integral $=\int \frac{-2 \cos x+3 \sin x}{4 \operatorname{oos} x+5 \sin x}$
$=\frac{-8+15}{16+25} x+\frac{-10-12}{16+25} \log (4 \cos x+5 \sin x) $

Questions from KCET 2022

1. For any integer $a$, the remainder obtained when $a^{2}$ is divided by $4$ is

2. It is observed that $23 x+17 y=1$ for some integers $x$ and $y$. Then $(x, y)=$

3. The sum of all the positive divisors of $180$ excluding $1$ and itself is

4. If $x+y+z=\pi$ then the value of $\begin{vmatrix}\sin (x+y+z) & \sin B & \cos z \\ -\sin B & 0 & \tan A \\ \cos (x+y) & -\tan A & 0\end{vmatrix}$ is

5. If the value of a third order determinant is $11 $ , then the value of the determinant formed by the cofactors will be

Mathematics Most Viewed Questions

1. The solution of $\frac{dy}{dx} = \frac{y}{x}+\tan \frac{y}{x}$ is

WBJEE 2011 Differential Equations

2. The solution of the differential equation $\frac{dy}{dx} = (x +y)^2$ is

COMEDK 2009 Differential Equations

3. If a and b are vectors such that $|a+b|=|a-b|$ then the angle between a and b is

KCET 2007 Vector Algebra

4. If $\begin{bmatrix}1&- \tan\theta \\ \tan \theta&1\end{bmatrix}\begin{bmatrix}1&\tan \theta \\ - \tan \theta &1\end{bmatrix}^{-1} = \begin{bmatrix}a&-b\\ b&a\end{bmatrix}$ then

COMEDK 2009 Matrices

5. $\int\frac{1}{\sin x\, \cos x}$ dx is equal to

KEAM 2016 Integrals

6. $\int\frac{\sin \frac{5x}{2}}{\sin \frac{x}{2}} dx $ is equal to :
(where $c$ is a constant of integration)

JEE Main 2019 Integrals

7. A particle is dropped under gravity from rest from a height $ h(g=9.8\,m/{{s}^{2}}) $ and it travels a distance $ \frac{9h}{25} $ in the last second the height $ h $ is:

Bihar CECE 2006

8. The value of $ \int{\frac{{{x}^{2}}+1}{{{x}^{4}}-{{x}^{2}}+1}}dx $ is

KEAM 2007 Integrals

9. The value of $\int \frac{x^2+1}{x^2-1}dx$ is

KCET 2007 Integrals

10. The value of the integral $\int\frac{cos x}{sin x + cos x}dx$ is equal to

KEAM 2013 Integrals

Latest Updates