List of top Mathematics Questions on Integration asked in AP EAMCET

Evaluate the integral: \[ \int \frac{1}{(1 + x^2) \sqrt{x^2 + 2}} \, dx. \]

 For all x ∈ [0, 2024] assume that f (x) is differentiable. f (0) = −2 and f ′(x) ≥ 5. Then the least possible value of f (2024) is:

Let f(x) = \(\int \frac{x}{(x^2+1)(x^2+3)} dx\). If f(3) = \(\frac{1}{4} \log(\frac{5}{6})\), then f(0) =

\(\int\frac{2\cos 2x}{(1+\sin 2x)(1+\cos 2x)}dx=\)

\(\int\left(\frac{x}{x\cos x - \sin x}\right)^2 dx = \)

If \(\lim_{n\rightarrow\infty}[(1+\frac{1}{n^{2}})(1+\frac{4}{n^{2}})(1+\frac{9}{n^{2}})\cdots(1+\frac{n^{2}}{n^{2}})]^{\frac{1}{n}}=ae^{b}\), then a+b=

Find the area enclosed by the curve \( y = x^3 - 19x + 30 \) and the X-axis.
Evaluate \( \int_{ \log 4}^{ \log 5} \frac{e^{2x} + e^x}{e^{2x} - 5e^x +6} dx \):
Evaluate the integral: \[ I = \int (\tan^7 x + \tan x) dx. \]
Evaluate the integral: \[ I = \int \frac{\csc x}{3\cos x + 4\sin x} dx. \]
Evaluate the integral: \[ \int \sin^{-1} \left( \sqrt{\frac{x - a}{x}} \right) dx \]
The parametric form of a curve is \(x=\dfrac{t^3}{t^2-1},\; y=\dfrac{t}{t^2-1}\), then \(\displaystyle \int \frac{dx}{x-3y}=\)
Assertion (A): If \(I_n=\int \cot^n x \, dx\), then \(I_6+I_4=\dfrac{-\cot^5 x}{5}\)
Reason (R): \[ \int \cot^n x \, dx=\frac{-\cot^{\,n-1}x}{n-1}-\int \cot^{\,n-2}x \, dx \]
If
\[ I_n=\int \tan^n x\,dx \] and
\[ I_0+I_1+2I_2+2I_3+2I_4+I_5+I_6=\sum_{k=1}^{n}\frac{\tan^k x}{k}, \] then \(n=\)
Evaluate
\[ \int \frac{e^{\cot x}}{\sin^2 x}\left(2\log\cosec x+\sin2x\right)\,dx \]