Mathematics

# If $\dfrac{d}{dx}\ f(x)=g(x)$ for $a\leq x\leq b$ then $\int_{b}^{a}f(x)g(x)dx$ equals to:

$\dfrac{[f(b)]^{2}-[f(a)]^{2}}{2}$

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

#### Realted Questions

Q1 Single Correct Hard
$\int { \cfrac { dx }{ \sqrt { { x }^{ 2 }+6x+5 } } } =$?
• A. $\log { \left| x+\sqrt { { x }^{ 2 }+6x+5 } \right| } +C\quad$
• B. $\log { \left| x-\sqrt { { x }^{ 2 }+6x+5 } \right| } +C$
• C. none of these
• D. $\log { \left| \left( x+3 \right) +\sqrt { { x }^{ 2 }+6x+5 } \right| } +C$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
If $\int\left(x^{2010}+x^{\text {804 }}+x^{402}\right)\left(2 x^{160 8}+5 x^{402}+10\right)^{1 / 402} d x$
$=\dfrac{1}{10 a}\left(2 x^{2010}+5 x^{804}+10 x^{402}\right)^{a / 402} .$ Then $(a-400)$ is equal to

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Hard
If $\displaystyle I= \int_{0}^{1}\frac{x dx}{8+x^{3}}$ then the smallest interval in which $I$ lies is
• A. $\displaystyle \left ( 0,\frac{1}{8} \right )$
• B. $\displaystyle \left ( 0,\frac{1}{10} \right )$
• C. $\displaystyle \left ( 0,\frac{1}{7} \right )$
• D. $\displaystyle \left ( 0,\frac{1}{9} \right )$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
$\displaystyle\int _ { 0 } ^ { \pi } \dfrac { x \sin x } { 1 + \cos ^ { 2 } x } d x =$
• A. $\frac { \pi ^ { 2 } } { 2 }$
• B. $\pi ^ { 2 }$
• C. $0$
• D. $\frac { \pi ^ { 2 } } { 4 }$

Evaluate :$\displaystyle \int \dfrac{dx}{x(x^2+1)}$