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Standalone Questions
#905 Mathematics Integrals
SA APPLY 2023
KNOWLEDGE 3 Marks
Find: $\int x^{2}\log(x^{2}+1)dx$
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#904 Mathematics Integrals
SA APPLY 2023
KNOWLEDGE 3 Marks
Find: $\int\frac{\cos x}{\sin 3x}dx$
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#903 Mathematics Integrals
SA APPLY 2023
KNOWLEDGE 3 Marks
Evaluate $\int_{1}^{e}\frac{1}{\sqrt{4x^{2}-(x\log x)^{2}}}dx$
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#902 Mathematics Integrals
SA APPLY 2023
KNOWLEDGE 3 Marks
Evaluate: $\int_{1}^{3}\frac{\sqrt{4-x}}{\sqrt{x}+\sqrt{4-x}}dx$
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#901 Mathematics Integrals
SA APPLY 2023
KNOWLEDGE 3 Marks
28. (b) OR: Evaluate: $\int_{0}^{\pi/2}\sqrt{\sin x}\cos^{5}x~dx$
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#900 Mathematics Integrals
SA APPLY 2023
KNOWLEDGE 3 Marks
28. (a) Find: $\int\frac{e^{x}}{\sqrt{5-4e^{x}-e^{2x}}}dx$
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#899 Mathematics Integrals
SA APPLY 2023
KNOWLEDGE 3 Marks
27. (b) OR: Evaluate: $\int_{-2}^{2}\frac{x^{2}}{1+5^{x}}dx$
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#898 Mathematics Integrals
SA APPLY 2023
KNOWLEDGE 3 Marks
27. (a) Evaluate: $\int_{\pi/4}^{\pi/2}e^{2x}(\frac{1-\sin 2x}{1-\cos 2x})dx$
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#897 Mathematics Integrals
SA APPLY 2023
KNOWLEDGE 3 Marks
26. Find: $\int\frac{x^{2}+x+1}{(x+1)^{2}(x+2)}dx$
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#896 Mathematics Integrals
SA APPLY 2023
KNOWLEDGE 3 Marks
Evaluate : $\int_{0}^{\frac{\pi}{2}}e^{x }\sin x~dx$.
OR
Find: $\int\frac{1}{\cos(x-a)\cos(x-b)}dx$
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#895 Mathematics Integrals
SA APPLY 2023
KNOWLEDGE 3 Marks
Find:$\int \frac{1}{\sqrt{x}(\sqrt{x}+1)(\sqrt{x}+2)} \, dx$
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#894 Mathematics Integrals
SA APPLY 2023
KNOWLEDGE 3 Marks
Evaluate $\int_{0}^{\frac{\pi}{2}}[\log(\sin~x)-\log(2\cos~x)]dx.$
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#893 Mathematics Integrals
LA APPLY 2023
KNOWLEDGE 5 Marks
Evaluate: $\int_ 0 ^{π/2} [\sin 2x \tan⁻¹(\sin x)] dx$
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#892 Mathematics Integrals
SA APPLY 2023
KNOWLEDGE 3 Marks
(a) Evaluate: $\int_0^{2\pi} \frac{1}{1 + e^{\sin x}} dx $
OR
(b) Find: $\int \frac{x⁴} { ((x-1)(x²+1))}dx.$
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#808 Mathematics Integrals
MCQ_SINGLE APPLY 2023
KNOWLEDGE 1 Marks
$\int\frac{2\cos 2x-1}{1+2\sin x}dx$ is equal to:
(A) $x-2\cos x+C$
(B) $x+2\cos x+C$
(C) $-x-2\cos x+C$
(D) $-x+2\cos x+C$
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#807 Mathematics Integrals
MCQ_SINGLE APPLY 2023
KNOWLEDGE 1 Marks
$\int 2^{x+2}dx$ is equal to :
(A) $2^{x+2}+C$
(B) $2^{x+2}\log 2+C$
(C) $\frac{2^{x+2}}{\log 2}+C$
(D) $2\cdot\frac{2^{x}}{\log 2}+C$
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#806 Mathematics Integrals
MCQ_SINGLE APPLY 2023
KNOWLEDGE 1 Marks
9. If $\int_{0}^{a}3x^{2}dx=8$, then the value of 'a' is :
(A) 2
(B) 4
(C) 8
(D) 10
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#805 Mathematics Integrals
MCQ_SINGLE APPLY 2023
KNOWLEDGE 1 Marks
8. $\int e^{5\log x}dx$ is equal to :
(A) $\frac{x^{5}}{5}+C$
(B) $\frac{x^{6}}{6}+C$
(C) $5x^{4}+C$
(D) $6x^{5}+C$
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#804 Mathematics Integrals
MCQ_SINGLE APPLY 2023
KNOWLEDGE 1 Marks
\int_{0}^{\frac{\pi}{6}}sec^{2}(x-\frac{\pi}{6})dx is equal to :
(A) \frac{1}{\sqrt{3}}
(B) -\frac{1}{\sqrt{3}}
(C) \sqrt{3}
(D) -\sqrt{3}
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#803 Mathematics Integrals
MCQ_SINGLE UNDERSTAND 2023
KNOWLEDGE 1 Marks
If \frac{d}{dx}(f(x))=log\~x, then f(x) equals :
(A) -\frac{1}{x}+C
(B) x(log\~x-1)+C
(C) x(log\~x+x)+C
(D) \frac{1}{x}+C
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