Mathematics

# If $\Delta (x)=\left| \begin{matrix} 1+x+2{ x }^{ 2 } & x+3 & 1 \\ x+2{ x }^{ 2 } & x & 3 \\ 3x+6{ x }^{ 2 } & 3x+11 & 9 \end{matrix} \right|$ then $\displaystyle \int^{1}_{0}\Delta (x)dx$ is

$\dfrac {176}{5}$

Its FREE, you're just one step away

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

#### Realted Questions

Q1 Multiple Correct Hard
If $\varphi (t)$ = $\begin{cases}1,\,\,\,\,\, 0\le t < 1 \\ 0 \,\,\,\,\,\,\, \text{otherwise} \end{cases}$ then
$\displaystyle \int ^{3000}_{-3000} \begin{pmatrix} \displaystyle \sum_{r' = 2014}^{2016} \varphi (t-r')\varphi(t-2016)\end{pmatrix} dt =$
• A. $0$
• B. Does not exist
• C. A real number
• D. $1$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
If $\displaystyle \int\frac{\cos x-\sin x}{\sqrt{8-\sin 2x}}dx=\sin^{-1}\left (\frac{\sin x+\cos x}{a}\right )+c$, then $a$ is equal to
• A. $2$
• B. $4$
• C. $5$
• D. $3$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
$\int \frac{sinx}{1+cosx}dx$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Find an anti derivative (or integral) of the given function by the method of inspection.
$(ax+b)^2$

1 Verified Answer | Published on 17th 09, 2020

Q5 Single Correct Medium
$\int {{{\sin }^4}x{{\cos }^3}xdx}$
• A. $\dfrac {5\sin^5x-7\sin ^7x}{35}+C$
• B. $\dfrac {7\sin^5x-3\sin ^7x}{21}+C$
• C. $\dfrac {5\sin^5x+5\sin ^7x}{25}+C$
• D. $\dfrac {7\sin^5x-5\sin ^7x}{35}+C$