Mathematics

# Integrate the following function with respect to $x$$x^{2}.\cos{(x^{3})}\sqrt{\sin^{7}{(x^{3})}}$

##### SOLUTION
$=\displaystyle \int x^e \cos x^3 \sqrt {\sin (x^3)}$
$\sin (x^3)=t$
$(3x^2) \cos (x^3)=dt /dx$
$=\dfrac {1}{3} \displaystyle \int (t)^{7/2} \ \Rightarrow \ \dfrac {12}{3(9)}t^{9/2}$
$=\dfrac {2}{27}(\sin ^{9/2}(x)^3)$

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

#### Realted Questions

Q1 Single Correct Medium
Evaluate : $\displaystyle\int^a_{-a}\sqrt{\dfrac{a-x}{a+x}}dx$
• A. $\dfrac{a\pi}{2}$
• B. $2a\pi$
• C. None of these
• D. $a\pi$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Hard
$\int { \cfrac { 2{ x }^{ 3 } }{ \left( 4+{ x }^{ 8 } \right) } } dx=$?
• A. $\cfrac { 1 }{ 2 } \tan ^{ -1 }{ \cfrac { { x }^{ 4 } }{ 2 } } +C$
• B. $\cfrac { 1 }{ 2 } \tan ^{ -1 }{ { x }^{ 4 } } +C\quad$
• C. none of these
• D. $\cfrac { 1 }{ 4 } \tan ^{ -1 }{ \cfrac { { x }^{ 4 } }{ 2 } } +C\quad$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Hard
Integrate
$\int {\frac{{2\sin 2x - \cos x}}{{6 - {{\cos }^2}x - 4{\mathop{\rm sinx}\nolimits} }}dx}$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Evaluate, $y=\int e^{3a.logx}+e^{3x.loga}dx$

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