Evaluate: $\int \sqrt{\sec\frac{x}{2} - 1} \\, dx$ [Application]
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Integrals - ISC Class 12 Mathematics Questions with Answers, Page 3
105 past-paper questions on Integrals from ISC Class 12 Mathematics papers (2027-2017), newest first, in full. Questions 41-60 are on this page, 20 to a page. Tap "Show answer" under a question to see its answer.
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Evaluate: $\int e^x \left(\frac{1+x}{(2+x)^2}\right)\,dx$
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Evaluate $\int_{-a}^a x f(x)\,dx$ given, $f(x) = x + g(x)$ where $g(x)$ is an even function.
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Statement I: $\int_{-2}^2 \frac{x^2}{1 + 2^x} \, dx = \frac{8}{3}$.
Statement II: $\int_{-a}^a f(x) \, dx = 2 \int_0^a f(x) \, dx$, if $f(x)$ is an even function.
- (a)Both the statements are true.
- (b)Both the statements are false.
- (c)Statement I is false, and statement II is true.
- (d)Statement I is true, and statement II is false.
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Evaluate: $\int \frac{\tan\frac{x}{4}}{1 - \sin\frac{x}{4}} \, dx$.
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Evaluate: $\int (\log x)^2\,dx$
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Evaluate: $\int_0^\pi (\sin^4 x + \cos^4 x) \\, dx$
Hence evaluate: $\int_{-2\pi}^{2\pi} \frac{\sin^4 x + \cos^4 x}{1 + e^x} \\, dx$ [Evaluate]
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Evaluate the following integral: $\int \left(\frac{\cot x + \cot^3 x}{1 + \cot^3 x}\right) \, dx$.
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Evaluate: $\int_0^{\sqrt{2}} [x^2] \\, dx$ [Evaluate]
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Evaluate: $\int_0^{\pi/2} \log\tan x\,dx$
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If $\int (\cot x - \operatorname{cosec}^2 x)e^x dx = e^x f(x) + c$ then $f(x)$ will be:
- (a)$\cot x + \operatorname{cosec} x$
- (b)$\cot^2 x$
- (c)$\cot x$
- (d)$\operatorname{cosec} x$
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The value of $\int_1^{\sqrt{3}} \frac{dx}{1 + x^2}$ is:
- (a)$\frac{\pi}{2}$
- (b)$\frac{2\pi}{3}$
- (c)$\frac{\pi}{6}$
- (d)$\frac{\pi}{12}$
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Evaluate: $\int x^2 \cos x dx$
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Evaluate: $\int \frac{x + 7}{x^2 + 4x + 7} dx$
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Evaluate: $\int_0^6 |x + 3| dx$
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Evaluate: $\int_0^{2\pi} \frac{1}{1 + e^{\sin x}} dx$
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Evaluate: $\int_0^1 |2x + 1|\,dx$
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Evaluate: $\int_{-1}^1 x^{17}\cos^4 x\,dx$
- (a)$\infty$
- (b)$1$
- (c)$-1$
- (d)$0$
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Evaluate: $\int_0^{\frac{\pi}{2}} \frac{a \sin x + b \cos x}{\sin x + \cos x} \\, dx$
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Evaluate: $\int \frac{1 + \cos x}{\sin^2 x}\,dx$
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