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

Difficulty

Easy Medium Hard

Question 1

Paper 1, no calculatorEasy5 marks

The derivative of a function $f$ is

f'(x)=6x+2,\qquad x\in\mathbb{R},

and $f(0)=3$

(a)

Determine $f(x)$

[4]

(b)

Hence write down a definite integral representing the area bounded by the graph $y=f(x)$ the $x$ -axis, $x=0$ and $x=2$ Do not evaluate the integral.

[1]

Question 2

Paper 1, no calculatorEasy7 marks

The curve $y=x^2-1$ the $x$ -axis and the lines $x=-2$ and $x=2$ bound several regions.

(a)

Write down, without evaluating, an expression in terms of definite integrals for the total area of these regions.

[3]

(b)

Hence determine the exact total area of these regions.

[4]

Question 3

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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