IB Maths AA SL 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.

Paper

Paper 1, no calculator Paper 2, calculator

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Question 1

Paper 2, calculatorMedium6 marks

The curve $C$ has equation $y=f(x)$ where

f(x)=x^2-x-2.

(a)

Find the $x$ -coordinates of the points where $C$ intersects the $x$ -axis.

[2]

(b)

Consider the region between $C$ and the $x$ -axis from $x=-2$ to $x=3$

(i)

Write down an expression, as a sum or difference of definite integrals of $f$ for the total area of this region. Do not use absolute-value notation.

[2]

(ii)

Hence determine the total area exactly.

[2]

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