Mathematics

$\displaystyle\int_{0}^{1} x^2-3x \ dx$

SOLUTION

$=\displaystyle\int_{0}^{1} x^2-3x \ dx$

$=\left. \dfrac {x^3}3-3\dfrac {x^2}{2}\right]_0^1$

$=\dfrac 13-\dfrac 32$

$=\dfrac {2-9}6$

$=\dfrac {-7}6$

Its FREE, you're just one step away

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

Realted Questions

Q1 Single Correct Medium
$\lim_\limits{n \to \infty}\left[ \dfrac{1}{n^2} \sec^2\dfrac{1}{n^2} +\dfrac{2}{n}\sec^2\dfrac{4}{n^2}............+\dfrac{1}{n} \sec^21 \right]$
• A. $\dfrac{1}{2} \sec 1$
• B. $\dfrac{1}{2} \text{cosec} 1$
• C. $\tan 1$
• D. $\dfrac{1}{2}\tan 1$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
lf $f(x)=\left\{\begin{array}{l}e^{\cos x}\sin x, for |x|\leq 2\\2 ; otherwise\end{array}\right.$, then $\displaystyle \int_{-2}^{3}f(x)dx$ is
• A. $0$
• B. $1$
• C. $3$
• D. $2$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
$\int _{ 0 }^{ \pi /2 }{ \cfrac { \cos { 2x } }{ { \left( \sin { x } +\cos { x } \right) }^{ 2 } } } dx=......$
• A. $\cfrac { \pi }{ 4 }$
• B. $\cfrac { \pi }{ 2 }$
• C. $-\cfrac { \pi }{ 4 }$
• D. $0$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Solve $\displaystyle\int\dfrac{x}{{\sqrt {{a^2} + {x^2}} }}dx$

If $f(x+f(y))=f(x)+y \space\forall x, y \in R$ and $f(0)=1$, then prove that $\int_{0}^{2} f(2-x) d x=2 \int_{0}^{1} f(x) d x$