Mathematics

# Integrate :$\sin \left( {ax + b} \right)\cos \left( {ax + b} \right)$

##### SOLUTION
$\sin { (ax+b) } \cos { (ax+b) } \\ \frac { 1 }{ 2 } (2\sin { (ax+b) } \cos { (ax+b) } )\\ \frac { 1 }{ 2 } \{ \sin { 2ax+2b } \} \\ { I }=\frac { 1 }{ 2 } \int { \{ \sin { 2ax+2b } } \} { dx }\\ =\frac { 1 }{ 4a } (-\cos { (2ax))}+bx+C$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 111

#### Realted Questions

Q1 Single Correct Medium
$\int _{ 0 }^{ \pi /2 }{ \sin { 2x } .\sin { x } } dx=.....$
• A. $\cfrac{1}{3}$
• B. $-\cfrac{2}{3}$
• C. $\cfrac{4}{3}$
• D. $\cfrac{2}{3}$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Integrate $\int {({{\sin }^{ - 1}}} x{)^2}dx$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
If $\displaystyle \frac{x}{(x-3)(x-2)}= \frac{3}{x-3}+\frac{A}{x-2}$, then $A$=
• A. $1$
• B. $2$
• C. $-1$
• D. $-2$

1 Verified Answer | Published on 17th 09, 2020

Q4 Passage Medium
If the integrand is rational function of $x$ and fractional powers of a linear fractional function of the form $\dfrac {ax + b}{cx + d}$, then rationalisation of the integral is affected by the substitution $\displaystyle \frac {ax + b}{cx + d} = t^{m}$, where $m$ is $l.c.m$ of fractional powers of $\dfrac {ax + b}{cx + d}$.

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 $\displaystyle f(x)>0 \forall x \in R$