Question Text
Question 2 :
If the curves $y=x^3+ax$ and $y=bx^2+c$ pass through the point $(-1, 0)$ and have common tangent line at this point, then the value of $a+b$ is?
Question 3 :
The area bounded by the curve $y = f\left( x \right)$, above the $x$-axis, between $x = a$ and $x = b$ is:
Question 4 :
If the area bounded by the x-axis, curve $y=f(x)$ and the lines $x=1$, $x=b$ is equal to $\sqrt{b^2+1}-\sqrt{2}$ for all $b > 1$, then $f(x)$ is
Question 5 :
Points of inflexion of the curve<br>$y = x^4 - 6x^3 + 12x^2 + 5x + 7$ are
Question 14 :
$\displaystyle \int \cos \left \{ 2\tan ^{-1}\sqrt{\frac{1-x}{1+x}} \right \}dx$ is equal to
Question 15 :
If $f'(x) = x + \dfrac {1}{x}$, then value of $f(x)$ is
Question 16 :
Integrate the following functions with respect to t: $\displaystyle \int \left ( 3t^{2}-2t \right )dt$<br/>
Question 19 :
$\int \dfrac {x^{2} - 1}{x^{4} + 3x^{2} + 1} dx (x > 0)$ is
Question 20 :
If $\int \sin x d (\sec  x) = f(x) - g(x) + c$, then