Mathematics

# If $\int _{ 0 }^{ f\left( x \right) }{ { t }^{ 2 }dt=x\cos { \pi x } }$, then $f(9)$:

$-3$

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

#### Realted Questions

Q1 Single Correct Medium
$\displaystyle \overset{1}{\underset{0}{\int}} \sin \left(2\tan^{-1} \sqrt{\dfrac{1 - x}{1 + x}}\right)dx =$
• A. $\dfrac{\pi}{2}$
• B. $\dfrac{\pi}{3}$
• C. $\dfrac{\pi}{4}$
• D. $\pi$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
The value of $\sum\limits_{r = 1}^n {\int\limits_0^1 {f(r - 1 + x)} dx}$ is equal to (if function has period 1)
• A. $\int\limits_0^1 {f(x)} dx$
• B. $n\int\limits_0^1 {f(x)} dx$
• C. $(n - 1)\int\limits_0^1 {f(x)} dx$
• D. $\int\limits_0^n {f(x)} dx$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Hard
Evaluate: $\displaystyle \int \dfrac{1}{9x^2+ 49} dx$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
$\overset { 4 }{ \underset { -4 }{ \int } }$ log $\left(\dfrac{9 - x}{9 + x}\right)$ dx equals.
• A. -4
• B. 8
• C.
• D. 4

Let $g(x)$ be a function defined on $[0, 7]$ and $g(x)=\int_0^x f(t) dt$, where $y=f(x)$ is the function whose graph is as shown in figure given below, then