Evaluate: $\int \frac{2}{(1 - x)(1 + x^2)}\,dx$
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Integrals - ISC Class 12 Mathematics Questions with Answers, Page 4
105 past-paper questions on Integrals from ISC Class 12 Mathematics papers (2027-2017), newest first, in full. Questions 61-80 are on this page, 20 to a page. Tap "Show answer" under a question to see its answer.
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Evaluate: $\int \frac{1}{\sin^4 x + \cos^4 x} \\, dx$
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Evaluate: $\int_{-1}^2 |x^3 - x| \\, dx$
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Evaluate: $\int \cos^{-1}(\sin x)\,dx$
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Evaluate: $\int \frac{x}{x^2 + 1}\,dx$
- (a)$2\log(x^2 + 1) + c$
- (b)$\frac{1}{2}\log(x^2 + 1) + c$
- (c)$e^{x^2 + 1} + c$
- (d)$\log x + \frac{x^2}{2} + c$
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Evaluate: $\int [\sin(\log x) + \cos(\log x)] \\, dx$
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If $\int \log 2x \\, dx = x \log 2x - k + c$ where $k$ is a function of $x$, then find $k$.
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Evaluate: $\int \sqrt{\csc x - 1} \\, dx$
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If $\int x^5 \cos(x^6)\,dx = k \sin(x^6) + C$, find the value of $k$.
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Evaluate: $\int \frac{3e^{2x} - 2e^x}{e^{2x} + 2e^x - 8}\,dx$
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Evaluate: $\int \log_{10} x \, dx$
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Evaluate: $\int_{2}^{8} \frac{\sqrt{10-x}}{\sqrt{x} + \sqrt{10-x}} \, dx$
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Evaluate: $\int \frac{x^3 - x^2 + x - 1}{x - 1} \, dx$
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Evaluate: $\int \frac{dx}{\sin x + \sin 2x}$
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$\int_{0}^{2a} f(x) \, dx = \int_{0}^{a} f(x) \, dx + \int_{0}^{a} f(k-x) \, dx$, then the value of $k$ is:
- (a)$a$
- (b)$2a$
- (c)Independent of $a$
- (d)None of the above options
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If $\int \frac{(\log x)^2}{x} \, dx = \frac{(\log x)^k}{k} + c$, then the value of $k$ is:
- (a)3
- (b)2
- (c)1
- (d)None of the above options
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Evaluate: $\int_{0}^{\frac{\pi}{4}} \log(1 + \tan x) \, dx$
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Evaluate: $\int \frac{1 + \sin x}{1 - \sin x} \, dx$
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Given $\int e^x \left(\frac{x-1}{x^2}\right) \, dx = e^x f(x) + c$. Then $f(x)$ satisfying the equation is:
- (a)$x$
- (b)$x^2$
- (c)$\frac{1}{x}$
- (d)None of the above options
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Evaluate: $\int_{-6}^3 |x + 3| dx$
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