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Integral Calculus Preparation
English 5 leveled MCQs Free
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7 marks Long answer
Derive the reduction formula for $\int \sin^n x \, dx, \quad n \geq 2$
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The reduction formula is derived using integration by parts.
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5 marks Long answer
Explain the fundamental theorem of calculus.
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It connects differentiation and integration, stating that if $F$ is an antiderivative of $f$, then $\int_a^b f(x) \, dx = F(b) - F(a)$.
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4 marks Medium answer
Evaluate indefinite integrals using integration by parts.
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Use the formula $\int u \, dv = uv - \int v \, du$.
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4 marks Medium answer
Evaluate improper integrals.
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Determine limits and evaluate as $\lim_{b \to \infty} \int_a^b f(x) \, dx$.
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3 marks Medium answer
Explain the Net Change Theorem.
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It states that the net change in a quantity is equal to the integral of its rate of change over an interval.
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