Download App

Integrals — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsIntegrals1 Mark
Question
Find $\int x \cos x d x$
✓

Answer

Put f (x) = x (first function) and g (x) = cos x (second function).
Then, integration by parts gives
$\int x \cos x d x=x \int \cos x d x-\int\left[\frac{d}{d x}(x) \int \cos x d x\right] d x$ 
= $x \sin x-\int \sin x d x=x \sin x+\cos x+\mathrm{C}$ 

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 "1 Marks" from Integrals→Integrals — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Refer to Exercise 7 above. Find the maximum value of Z.
→
Find the principal value of the following:
$\sin^{-1}\Big(-\frac{\sqrt3}{2}\Big)$
→
Determine the order and degree of the following differential equations. state also whether they are linear or non linear.
$\Big(\frac{\text{d}^2\text{y}}{\text{dx}^2}\Big)^2+\Big(\frac{\text{dy}}{\text{dx}}\Big)^2=\text{x}\sin\Big(\frac{\text{d}^2\text{y}}{\text{dx}}\Big)$
→
Consider two points P and Q with position vectors $\vec{OP}=3 \vec{a}-2 \vec{b}$ and $\vec{OQ}=\vec{a}+\vec{b}$. Find the position vector (internally) of a point R which divides the line joining P and Q in the ratio 2 : 1.
→
Evaluate the following:
$\cot^{-1}\Big(\cot\frac{9\pi}{4}\Big)$
→
Write an anti derivative of function using the method of inspection: 3x2 + 4x3
→
Find $'\lambda'$ when the projection of $\overrightarrow{a}$ = $\lambda$$\hat{\text{i}}+\hat{\text{j}}+\hat{\text{4k}}$ on $\overrightarrow{b}=\hat{\text{2i}}+\hat{\text{6j}}+\hat{\text{3k}}\text{ is 4 units.}$
→
Let L be the set of all lines in a plane and R be the relation in L defined as R = {(L1, L2 ) : L1 is perpendicular to L2}. Show that R is symmetric but neither reflexive nor transitive.
→
Write the degree of the differrntial equation $\Big(1+\frac{\text{dy}}{\text{dx}}\Big)^{3}=\Big(\frac{\text{d}^{2}\text{y}}{\text{dx}^{2}}\Big)^{2}.$ 
→
State which of the following are not the probability distributions of a random variable. Give reasons for your answer.
Z 3 2 1 0 -1
P(Z) 0.3 0.2 0.4 0.1 0.05
→