Mathematics

# Solve:$\displaystyle \int{\sin 3x\cos 4x dx}$

##### SOLUTION

We have,

$\int{\sin 3x\cos 4x dx}$

On multiply and divide by 2 and we get,

$\int{\dfrac{2}{2}\sin 3x\cos 4x}dx$

$\Rightarrow \dfrac{1}{2}\int{2\sin 3x\cos 4x dx}$

Now using formula,

$2\sin A\cos B=\sin \left( A+B \right)+\sin \left( A-B \right)$

So,

$\Rightarrow \dfrac{1}{2}\int{\left[ \sin \left( 3x+4x \right)+\sin \left( 3x-4x \right) \right]}dx$

$\Rightarrow \dfrac{1}{2}\int{\left[ \sin 7x-\sin x \right]}dx$

$\Rightarrow \dfrac{1}{2}\int{\sin 7xdx-\dfrac{1}{2}\int{\sin xdx}}$

$\Rightarrow \dfrac{1}{2}\left( -\dfrac{\cos 7x}{7} \right)-\dfrac{1}{2}\left( -\cos x \right)+C$

$\Rightarrow -\dfrac{\cos 7x}{14}+\dfrac{1}{2}\cos x+C$

Hence, this is the answer.

Its FREE, you're just one step away

Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

#### Realted Questions

Q1 Single Correct Medium
Evaluate the given integral.
$\displaystyle\int { \cfrac { \sin ^{ 6 }{ x } }{ \cos ^{ 8 }{ x } } } dx$
• A. $\tan { 7x } +C$
• B. $\cfrac { \tan { 7x } }{ 7 } +C$
• C. $\sec ^{ 7 }{ x } +C\quad \quad$
• D. $\cfrac { \tan ^{ 7 }{ x } }{ 7 } +C$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Hard
If $l(m, n) = \int_0^1 t^m (1 + t)^n dt$, then the expression for $l(m, n)$ in terms of $l(m + 1, n - 1)$ is
• A. $\dfrac{n}{m + 1}. l (m + 1, n - 1)$
• B. $\dfrac{2n}{m + 1} + \dfrac{n}{m + 1} l. (m + 1, n - 1)$
• C. $\dfrac{m}{n + 1} . l (m + 1, n - 1)$
• D. $\dfrac{2^n}{m + 1} - \dfrac{n}{m + 1} .l(m + 1, n - 1)$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
$\int \dfrac { \sin 2 x } { 1 + \sin ^ { 2 } x }$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Integrate the function    $\displaystyle \frac {x^2+x+1}{(x+1)^2(x+2)}$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q5 Passage Medium
Consider two differentiable functions $f(x), g(x)$ satisfying $\displaystyle 6\int f(x)g(x)dx=x^{6}+3x^{4}+3x^{2}+c$ & $\displaystyle 2 \int \frac {g(x)dx}{f(x)}=x^{2}+c$. where $\displaystyle f(x)>0 \forall x \in R$

On the basis of above information, answer the following questions :

Asked in: Mathematics - Limits and Derivatives

1 Verified Answer | Published on 17th 08, 2020