Download App

Integrals — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSIntegrals1 Mark
Question
Evaluate: $\int[\sin (\log x)+\cos (\log x)] d x$
✓

Answer

(a) : Let $I=\int[\sin (\log x)+\cos (\log x)] d x$
Put $\log x=t \Rightarrow x=e^t \quad \Rightarrow d x=e^t d t$
$
\begin{aligned}
\therefore \quad I & =\int(\sin t+\cos t) e^t d t=e^t \sin t+C \\
& =x \sin (\log x)+C\left[\because\left[f(x)+f^{\prime}(x)\right] e^x d x=e^x f(x)+C\right)
\end{aligned}
$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from Integrals→Integrals — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

The altitude of a cone is 20cm and its semi-vertical angle is 30°. If the semi-vertical angle is increasing at the rate of 2° per second, then the radius of the base is increasing at the rate of:
  1. $30\text{cm}/\text{sec}.$
  2. $\frac{160}{3}\text{cm}/\text{sec}.$
  3. $10\text{cm}/\text{sec}.$
  4. $160\text{cm}/\text{sec}.$
→
For any square matrix $A, A A^T$ is a
→
The general solution of differential equation is $(y + c)^2= cx$ where ccis an arbitrary constant. The order and degree of the differential equation are respectively:
→
Let f : R → R be a function defined by $\text{f(x)}=\frac{\text{e}^{|\text{x}|}-\text{e}^{-\text{x}}}{\text{e}^{\text{x}}+\text{e}^{-\text{x}}}.$ Then,
  1. f is a bijection.
  2. f is an injection only.
  3. f is surjection on only.
  4. f is neither an injection nor a surjection.
→
Choose the correct answer from the given four options.
The value of $\cot\Big[\cos^{-1}\Big(\frac{7}{25}\Big)\Big]$ is:
  1. $\frac{25}{24}$
  2. $\frac{25}{7}$
  3. $\frac{24}{25}$
  4. $\frac{7}{24}$
→
$\int\limits^\pi_0\sqrt{\frac{1-\text{x}}{1+\text{x}}}\text{ dx}=$
  1. $\sqrt{1-\pi^2}-1$
  2. $\frac{\pi}{2}-1$
  3. $\frac{\pi}{2}+1$
  4. ${\pi}+{1}$
→
The function $\text{f(x)}=|\cos\text{x}|$ is:
  1. Differentiable at$\text{x}=(2\text{n}+1)\frac{\pi}{2},\text{n}\in\text{Z}$
  2. Continuous but not differentiable at $\text{x}=(2\text{n}+1)\frac{\pi}{2},\text{n}\in\text{Z}$
  3. Neither differentiable nor continuous at $\text{x}=\text{n}\in\text{Z}$
  4. None of these.
→
$\int_0^{\pi / 2} \frac{\sin x-\cos x}{1+\sin x \cos x} d x$ is equal to :
→
In the interval (1, 2), function f(x) = 2|x - 1| + 3|x - 2| is:
  1. Monotonically increasing.
  2. Monotonically decreasing.
  3. Not monotonic.
  4. Constant.
→
If $c_{i j}$ is the cofactor of the element $a_{i j}$ of the determinant $\left|\begin{array}{ccc}2 & -3 & 5 \\ 6 & 0 & 4 \\ 1 & 5 & -7\end{array}\right|$, then write the value of $a_{32} \cdot c_{32}$.
→