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Chapter 7 Class 12 Integrals | 5 questions | about 4 minutes

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Question 1 of 5
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Question 1 of 5
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If \(f\) and \(g\) are continuous functions in \([0,1]\) satisfying \(f(x)=f(a-x)\) and \(g(x)+g(a-x)=a\), then \(\int_0^a f(x) \cdot g(x) d x\) is equal to
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Question 2 of 5
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If \(\int_0^1 \frac{e^t}{1+t} d t=a\), then \(\int_0^1 \frac{e^t}{(1+t)^2} d t\) is equal to
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Question 3 of 5
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\( \int_{-1}^1 \frac{x^3+|x|+1}{x^2+2|x|+1} d x\) is equal to
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Question 4 of 5
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If \(x=\int_0^y \frac{d t}{\sqrt{1+9 t^2}}\) and \(\frac{d^2 y}{d x^2}=a y\), then \(a\) is equal to
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Question 5 of 5
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If \(\int \frac{x^3 d x}{\sqrt{1+x^2}}=a\left(1+x^2\right)^{\frac{3}{2}}+b \sqrt{1+x^2}+\mathrm{C}\), then
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