Download App

Indefinite Integrals — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSIndefinite Integrals2 Marks
Question
Evaluate the following integrals:
$\int\text{x}\cos\text{x dx}$
✓

Answer

Let $\text{I}=\int\text{x}\cos\text{x dx}$
Using integration by parts,
$\text{I}=\text{x}\int\cos\text{x dx}-\int(1\times\int\cos\text{x dx})\text{dx+C}$
$=\text{x}\sin\text{x}-\int\sin\text{x dx+C}$
$\text{I}=\text{x}\sin\text{x}+\cos\text{x+C}$

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 "2 Marks Questions" from Indefinite Integrals→Indefinite Integrals — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Let * be a binary operation on Z defined by a * b = a + b - 4 for all a, b ∈ Z.
Find the invertible elements in Z.
→
If the $\vec{\text{a}}$ and $\vec{\text{b}}$ are such that $|\vec{\text{a}}|=3,\big|\vec{\text{b}}\big|=\frac{2}{3}$ and $\vec{\text{a}}\times\vec{\text{b}}$ is a unit vector, then the angle between $\vec{\text{a}}$ and $\vec{\text{b}}.$
→
Evaluate $\int\frac{\sec^2\sqrt{\text{x}}}{\sqrt{\text{x}}}\text{ dx}$
→
Find the scalar and vector components of the vector with initial point (2, 1) and terminal point (–5, 7).
→
Find all the points of discontinuity of the function f defined by $f(x)=\left\{\begin{array}{cc} {x+2,} & {\text { if } x<1} \\ {0,} & {\text { if } x=1} \\ {x-2,} & {\text { if } x>1} \end{array}\right.$
→
Prove that the function $\text{f}(\text{x})=\cos\text{x}$ is:
Strictly increasing in $(\pi,2\pi)$
→
Which is greater$, \tan 1$ or $\tan ^{-1} 1 ?$
→
Evaluate the following definite integrals:
$\int_{-2}\limits^{\frac{1}{2}}\frac{1}{\sqrt{1-\text{x}^2}} \text{ dx}$
→
Verify that the function y = cos x + C (explicit or implicit) is a solution of differential equation y' + sin x = 0.
→
Evaluate the following integrals:
$\int\Big\{3\sin\text{x}-4\cos\text{x}+\frac{5}{\cos^2\text{x}}-\frac{6}{\sin^2\text{x}}+\tan^2\text{x}-\cot^2\text{x}\Big\}\text{dx}$
→