Download App

INTEGRALS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsINTEGRALS3 Marks
Question
Evaluate: $\int \cos \text{4 x} \cos 3\text{x dx}$
✓

Answer

$\text{I} = \int \cos \text{4 x} \cos 3\text{x dx} = \frac{1}{2} \int(\cos 7x + \cos x) \text{dx}$$= \frac{1}{2} \bigg[ \frac{\sin 7x}{7} + \sin x\bigg] + c$or $\frac{1}{14} \sin 7 x + \frac{1}{2} \sin x + c$

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 "3 Marks Question" 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

A laboratory blood test is 99% effective in detecting a certain disease when its infection is present. However, the test also yields a false positive result for 0.5% of the healthy person tested (i.e. if a healthy person is tested, then, with probability 0.005, the test will imply he has the disease). If 0.1% of the population actually has the disease, what is the probability that a person has the disease given that his test result is positive?
→
Find the equation of rthe planes parallel to the plane x + 2y - 2z + 8 = 0 that are at a distance of 2 units from the point (2, 1, 1).
→
Solve the following equation:$\cos(\tan^{-1}\text{x}) = \sin\bigg(\cot^{-1}\frac{3}{4}\bigg).$
→
Using vectors show that the points A(-2, 3, 5), B(7, 0, -1), C(-3. -2, -5) and D(3, 4, 7) are such that AB and CD intersect at the point P(1, 2, 3).
→
Dot product of a vector with vectore $\hat{\text{i}}-\hat{\text{j}}+\hat{\text{k}},2\hat{\text{i}}+\hat{\text{j}}-3\hat{\text{k}}$ and $\hat{\text{i}}+\hat{\text{j}}+\hat{\text{k}}$ are respectively 4, 0 and 2. Find the vector.
→
Write the minors and cofactors of element of the first column of the following matrices and hence evaluate the determinant in case:
$\text{A}=\begin{vmatrix}5&20\\0&-1 \end{vmatrix}$
→
Integrate the function $\frac{{{x^2}}}{{\sqrt {{x^6} + {a^6}} }}$
→
If $y=3 \cos x-2 \sin x$, then prove that $\frac{d^2 y}{d x^2}-y=0$
→
Examine the consistency of the system of equations:
3x - y - 2z = 2
2y - z = -1
3x - 5y = 3
→
Let $\vec{a}=i+4 j+2 k, b=3 i-2 j+7 k$ and $c=2 i-j+4 k$. Find a vector $d$ which is perpendicular to both $\vec{a}$ and $\vec{b}$, and $\vec{c} . \vec{d}=15$.
→