Integrals (Standard)

Integrals: core idea

• 1. Area under $y=x^2$ from $0$ to $2$?

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• 2. Evaluate $\int_0^{\pi}\sin^2 x\,dx$.

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• 3. Evaluate $\int_0^1 \dfrac{dx}{1+x^2}$.

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• 4. Evaluate $\int_0^1 (1-x)^3\,dx$.

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• 5. Evaluate $\int 2x\cos(x^2)\,dx$ as $\sin(x^2)+C$: coefficient of $\sin$?

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• 6. Evaluate $\int_1^e \ln x\,dx$.

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• 7. Evaluate $\int_0^1 x\sqrt{x}\,dx$.

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• 8. Average value of $x^2$ on $[0,3]$?

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• 9. Evaluate $\int_0^{\pi/4}\sec^2 x\,dx$.

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