List of top Mathematics Questions on Fundamental Theorem of Calculus asked in BITSAT

The area enclosed between the curve \(y = \log_e(x + e)\) and the coordinate axes is:
The area enclosed between the curve \(y = \log_e(x + e)\) and the coordinate axes is:
Evaluate the sum: $$ \sum_{n=1}^{\infty} \frac{1}{n(n+1)(n+2)} $$
If log$_{10}$(x + 1) = 2, what is the value of x?
Find the derivative of \( y = \sin(x^2) \) with respect to \( x \).
Evaluate: $$ \lim_{x \to 0} \frac{\sqrt{1 + x} - \sqrt{1 - x}}{x} $$
If $\log_2 (x-1) + \log_2 (x-3) = 3$, find the value(s) of $ x $.
Let $f(x)=\left(x^{5}-1\right)\left(x^{3}+1\right), g(x)=\left(x^{2}-1\right)\left(x^{2}-x+1\right)$ and let $h(x)$ be such that $f(x)=g(x) h(x)$. Then $\displaystyle\lim _{x \rightarrow 1} h(x)$ is
Find the coordinates of the point where the line joining the points $(2, -3, 1)$ and $(3, - 4, - 5)$ cuts the plane $2x + y + z = 7$.
What is the value of n so that the angle between the lines having direction ratios $(1, 1, 1)$ and $(1, -1, n)$ is $60^{\circ}$ ?
The foot of the perpendicular from the point $(7, 14, 5)$ to the plane $2x + 4y - z = 2$ are
$\int\limits_{0}^{\pi /4} \log (1 + \tan \, x ) dx$ is equal to :