Mathematics

# Find the integral of the function $\sin 3x\cos 4x$.

##### SOLUTION
for integrals of type $\sin ax\, \cos bx$
$\sin ax\ \cos bx =\dfrac{1}{2}\left( \sin(ax+bx)+\sin(ax-bx) \right )$
If $a=3$ $b=4$
$\sin 3x\ \cos 4x=\dfrac{1}{2}\left( \sin(7x)+\sin(-x) \right )$
$=\dfrac{1}{2}\left( \sin 7x-\sin x \right )$
$\displaystyle \int \sin 3x\cos 4 x \,dx = \dfrac{1}{2}\int \left(\sin 7x-\sin x \right )dx$
$=\dfrac{1}{2}\left(\dfrac{-1}{7}\cos 7x+\cos x \right )+c$

$=\dfrac{\cos x}{2}-\dfrac{-\cos 7x}{14}+c$

Its FREE, you're just one step away

Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

#### Realted Questions

Q1 Subjective Medium
Solve :
$\int e^{x^2+\text{ln x}} . dx$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Hard
Evaluate: $\displaystyle\int{\frac{5x^4+4x^5}{{(x^5+x+1)}^2}dx}$
• A. $x^5+x+1+C$
• B. $\displaystyle\frac{x^5}{x^5+x+1}+C$
• C. $x^{-4}+x^{-5}+C$
• D. $\displaystyle-\frac{x + 1}{x^5+x+1}+C$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Hard
Solve $\displaystyle \int \frac{x^{4}+4x^{3}+11x^{2}+12x+8}{(x^{2}+2x+3)^{2}(x+1)}dx$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
$\displaystyle \int (e^\sqrt[3]{x}dx)=$
• A. $x^{2/3}-2 x^{1/3} +2+c$
• B. $(x^{2/3} - 2x^{1/3} +2)\exp(\sqrt[3]{x})+c$
• C. $2(x^{2/3} - 2x^{1/3}+2)\exp(\sqrt[3]{x})+c$
• D. $3(x^{2/3} - 2x^{1/3}+2)\exp(\sqrt[3]{x})+c$

$\displaystyle\int\limits_{-1}^{1}xe^{x^2}\ dx$.