IB Maths AA HL AA 5.3 Integration questions

Exam-style questions in the shape of Paper 1 and Paper 2, with full markschemes. Read the markscheme, or type, photograph or draw your answer and get it marked.

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Paper 1, no calculator Paper 2, calculator

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Question 1

Paper 2, calculatorHard6 marks

For a real parameter $k>0$ let

f_k(x)=\frac{x^2-k}{x^2+1},\qquad -3\leq x\leq 3.

It is known that

\int_{-3}^{3} f_k(x)\,dx=0.

(a)

Determine the exact value of $k$

[2]

(b)

Hence determine the total area between the graph of $y=f_k(x)$ and the $x$ -axis for $-3\leq x\leq 3$ Show a definite-integral expression before evaluating. Do not use numerical integration. Give your answer to 3 significant figures.

[4]

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