Evaluate: 4x 3x dx. - Vidyadip

Question

Evaluate:$\int\sin\text{4x}\cos\text{3x dx}$.

✓

Answer

Writing I = $\frac{1}{2}\int2\sin\text{ 4x }\cos\text{ 3x dx}=\frac{1}{2}\int(\sin\text{7x}+\sin\text{x) dx}$$=\frac{1}{2}\Bigg[\frac{-\cos\text{ 7x}}{7}-\cos\text{x}\Bigg]+\text{c }\text{ OR }-\frac{1}{14}\cos\text{ 7x}-\frac{1}{2}\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 "3 Marks Question" 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

Prove that $\text{f(x)}=\sin\text{x}+\sqrt{3}\cos\text{x}$ has maximum value at $\text{x}=\frac{\pi}{6}.$

Evaluate the following integrals:
$\int\sqrt{\text{x}-\text{x}^2}\text{dx}$

Let $A = \{-1, 0, 1, 2\}, B = \{-4, -2, 0, 2\}$ and $f, g : A \rightarrow B$ be the functions defined by $f(x) = x^2 - x, x \in A$ and $g(x) = 2\left| {x - \frac{1}{2}} \right| - 1,x \in A.$ Are $f$ and $g$ equal? Justify your answer. $($Hint: One may note that two functions $f : A \rightarrow B$ and $g : A \rightarrow B$ such that$ f(a) = g(a) \forall$ a $\in A,$ are called equal functions$).$

Prove the following Exercise:
$\int^{1}_{0}\sin^{-1}\text{x dx}=\frac{\pi}{2}-1$

Let $\text{A}=\begin{bmatrix}2&-3\\-7&5\end{bmatrix}$ and $\text{B}=\begin{bmatrix}1&0\\2&-4\end{bmatrix},$ verify that
$(\text{A}+\text{B})^\text{T}=\text{A}^\text{T}+\text{B}^\text{T}$

If $\text{A}=\begin{bmatrix}\sin\alpha&\cos\alpha\\-\cos\alpha&\sin\alpha\end{bmatrix},$ verify that $A^TA = I_2$.

If $\text{y}=2\sin\text{x}+3\cos\text{x}$ Prove that $\frac{\text{d}^2\text{y}}{\text{dx}^2}+\text{y}=0$

If with reference to the right handed system of mutually perpendicular unit vectors $\hat i,\hat j$ and $\hat k$, $\vec \alpha = 3\hat i - \hat j$, $\vec \beta = 2\hat i + \hat j - 3\hat k$, then express $\vec \beta $ in the form $\vec \beta = {\vec \beta _1} + {\vec \beta _2}$, where ${\vec \beta _1}$ is || to $\vec \alpha $ and ${\vec \beta _2}$ is perpendicular to $\vec \alpha $.

Find the vector and cartesian equations of a plane passing through the point (1, -1, 1) and normal to the line joining the points (1, 2, 5) and (-1, 3, 1)

Show that $\text{AB}\neq\text{BA}$ in the following cases:
$\text{A}=\begin{bmatrix}1&3&0\\1&1&0\\4&1&0\end{bmatrix}$ and $\text{B}=\begin{bmatrix}0&1&0\\1&0&0\\0&5&1\end{bmatrix}$