Evaluate: $\int \frac{\cos x}{3\cos x - 5}\,dx$
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Integrals - ISC Class 12 Mathematics Questions with Answers, Page 2
105 past-paper questions on Integrals from ISC Class 12 Mathematics papers (2027-2017), newest first, in full. Questions 21-40 are on this page, 20 to a page. Tap "Show answer" under a question to see its answer.
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Evaluate: $\int \frac{dx}{x^{1/2} - x^{1/3}}$.
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Evaluate: $\int \frac{dx}{\sqrt[4]{(x-1)^3 (x+2)^5}}$.
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Evaluate: $\int_0^{\pi/2} \frac{\sqrt{\tan x}}{1 + \sqrt{\tan x}}\,dx$
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Evaluate: $\int \{f(ax+b)\}^n \cdot f'(ax+b) \, dx, n \neq -1$.
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Evaluate: $\int 2^{2^{2^x}} \cdot 2^{2^x} \cdot 2^x \, dx$.
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If $\int \left(\frac{2-x}{(x-1)^2}\right) e^x \, dx = e^x f(x) + c$, then $f(x)$ will be:
- (a)$\frac{1}{x-1}$
- (b)$\frac{1}{2-x}$
- (c)$\frac{1}{3-x}$
- (d)$\frac{1}{1-x}$
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Evaluate: $\int \frac{5}{\sqrt{2x+7}}\,dx$
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Evaluate: $\int 2^x [f'(x) + f(x)\log 2] \, dx$.
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Identify the correct answer of $\int_0^\pi \sin^{2024} x \cos^{2023} x \, dx$:
- (a)$0$
- (b)$1$
- (c)$2$
- (d)$3$
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Evaluate: $\int \frac{2x^3 - 1}{x^4 + x} \\, dx$ [Evaluate]
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Evaluate: $\int \frac{\cos x}{\sin^2 x + 4\sin x + 5}\,dx$
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Evaluate: $\int_{-\pi/2}^{\pi/2} \sin|x| \, dx$.
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Evaluate: $\int \frac{1}{\operatorname{cosec} x + \cot x}\,dx, x \neq 0$
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Evaluate: $\int \frac{dx}{(x-1)^2(x^2 + 1)^2}$
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If $\int x^3 5^{x^2}\,dx = K 5^{x^2} + C$, then find the value of $K$.
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Prove: $\int_0^{\frac{3\pi}{4}} \frac{x\,dx}{1 + \sin x} = (\sqrt{2} - 1)\pi$
Given: $\int_0^{\frac{3\pi}{4}} \frac{x\,dx}{1 + \sin x}$
To show: $(\sqrt{2} - 1)\pi$
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Evaluate: $\int x \tan^{-1} x\,dx$
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Evaluate: $\int e^x \csc x (1 - \cot x) \\, dx$ [Evaluate]
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$\int_0^1 \frac{x^4 - 1}{x^2 + 1}\,dx$ is equal to:
- (a)$\frac{2}{3}$
- (b)$\frac{1}{3}$
- (c)$-\frac{2}{3}$
- (d)$0$
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