CBSE Class 12 Maths Integrals Quiz 5

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1. Evaluate: ∫(2 tan x – 3 cot x)² dx

A -4tan x – cot x – 25x + C B 4 tan x – 9 cot x – 25x + C C – 4 tan x + 9 cot x + 25x + C D 4 tan x + 9 cot x + 25x + C

2. Evaluate: ∫ sec²(7 – 4x)dx

A –\(\frac{1}{4}\) tan(7 – 4x) + C B \(\frac{1}{4}\) tan(7 – 4x) + C C \(\frac{1}{4}\) tan(7 + 4x) + C D –\(\frac{1}{4}\) tan(7x – 4) + C

3. ∫ \(\frac{10x^9+10^xlog_e 10}{10^x+x^{10}}\) dx is equal to

A 10 – x + C B 10+ x+ C C (10– x)+ C D log (10+ x) + C

4. Evaluate: ∫ sec x cosec xdx

A \(\frac{3}{5}\) tan x – 3 tan x + C B –\(\frac{3}{5}\) tan x + 3 tan + C C –\(\frac{3}{5}\) tan x – 3 tan + C D None of these

5. ∫ \(\frac{a}{(1+x^2)tan^{-1}x}\) dx =

A a log |tan x| + C B \(\frac{1}{2}\)(tanx)² + C C a log (1 + x) + C D None of these

6. ∫ \(\frac{cot x}{\sqrt[3]{sin x}}\) dx =

A \(\frac{-3}{\sqrt[3]{sin x}}\) + C B \(\frac{-2}{sin^3 x}\) + C C \(\frac{3}{sin^{1/3}x}\) + C D None of these

7. Evaluate: ∫ \(\frac{1}{1+3sin^2x+8cos^2x}\) dx

A \(\frac{1}{6}\) tan(2 tan x) + C B tan(2 tan x) + C C \(\frac{1}{6}\) tan(\(\frac{2 tan x}{3}\)) + C D None of these

8. Evaluate: ∫ \(\frac{1}{\sqrt{9+8x-x^2}}\) dx

A -sin(\(\frac{x-4}{5}\)) + C B sin(\(\frac{x+4}{5}\)) + C C sin D None of these

9. ∫ \(\frac{dx}{1-cosx-sinx}\) is equal to

A log |1 + cot\(\frac{x}{2}\)| + C B log |1 – tan\(\frac{x}{2}\)| + C C log |1 – cot\(\frac{x}{2}\)| + C D log |1 + tan\(\frac{x}{2}\)| + C

10. Evaluate: ∫ \(\frac{1}{\sqrt{1-e^{2x}}}\) dx

A log |e + \(\sqrt{e^{-2x} – 1}\)| + C B -log |e + \(\sqrt{e^{-2x} – 1}\)| + C C -log |e– \(\sqrt{e^{-2x} – 1}\)| + C D None of these

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