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Definite Integrals — CBSE Class 12 board PYQs

54 past board questions on Definite Integrals, arranged like the paper itself — objective first, long answers last, newest year first in each section. Open any question for its complete solution.

Multiple Choice2 Qs

The value of $\int_{π /4}^{π /2} cot θ cosec^{2} θ d θ$ is
CBSE 2024View solution →
$\int_{- \frac{π}{4}}^{\frac{π}{4}} sec^{2} x d x$ :
CBSE 2020View solution →

Very Short Answer13 Qs

Evaluate $\int_{1}^{3} ∣2 x - 1∣ d x$ .
CBSE 2020View solution →
Evaluate: $\int_{2}^{3} 3^{x} d x$
CBSE 2017View solution →
If $f (x) = \int_{0}^{x} t sin t d t$ , then write the value of $f^{'} (x)$ .
CBSE 2014View solution →
Evaluate $\int_{2}^{3} \frac{1}{x} d x$
CBSE 2012View solution →
Evaluate : $\int_{0}^{1} \frac{d x}{1 - x ^{2}}$
CBSE 2011View solution →
Write the value of $\int_{0}^{1} \frac{1}{2 x + 3} d x$
CBSE 2011View solution →
Write the value of $\int_{0}^{1} \frac{2 x}{1 + x ^{2}} d x$
CBSE 2011View solution →
Evaluate: $\int_{- \frac{π}{2}}^{\frac{π}{2}} sin^{5} x d x$
CBSE 2011View solution →
If $\int_{0}^{1} (3 x^{2} + 2 x + k) d x = 0$ , find the value of $k$ .
CBSE 2009View solution →
Evaluate: $\int_{0}^{1} \frac{d x}{1 + x ^{2}}$
CBSE 2008View solution →
Using properties of definite integrals, prove that $\int_{\frac{π}{6}}^{\frac{π}{3}} \frac{d x}{1 + t a n x} = \frac{π}{12}$
CBSE 2007View solution →
Using properties of definite integrals, prove that $\int_{0}^{2} x 2 - x d x = \frac{16 2}{15}$
CBSE 2007View solution →
$\int_{0}^{2} 4 - x^{2} d x$
CBSE 2006View solution →

Short Answer4 Qs

Long Answer35 Qs