IB Mathematics Analysis and Approaches Topic SL 5.11—definite Integrals, Areas Under Curve Onto X-axis and Areas Between Curves Questionbank (SL/HL)

IB Mathematics Analysis and Approaches Topic SL 5.11—definite Integrals, Areas Under Curve Onto X-axis and Areas Between Curves Questionbank (SL/HL) | RevisionDojo

Practice IB Mathematics Analysis and Approaches (AA) Topic SL 5.11—definite Integrals, Areas Under Curve Onto X-axis and Areas Between Curves with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for SL 5.11—definite Integrals, Areas Under Curve Onto X-axis and Areas Between Curves and mirrors Paper 1, 2, 3 style where relevant.

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Paper

Level

Question 1

HLPaper 1

Consider the function $f (x) = e^{- x} tan x$ defined for $0 \leq x < \frac{π}{2}$ .

Find an expression for $f^{'} (x)$ .

[3]

Hence, find the exact value of $\int_{0}^{\frac{π}{4}} e^{- x} (sec^{2} x - tan x) d x$ .

[3]

Question 2

SLPaper 1

The velocity, $v$ , in $m s^{- 1}$ , of a particle moving along a straight line at time $t$ seconds is given by $v (t) = 6 t^{2} - 12 t + 5$ , for $0 \leq t \leq 2$ .

Find the acceleration of the particle at time $t$ (in $m s^{- 2}$ ).

[2]

Find the total distance traveled by the particle from $t = 0$ to $t = 2$ .

[5]

Question 3

SLPaper 2

Consider the functions $f (x) = e^{x} - 1$ and $g (x) = 2 - x^{2}$ .

Find the x-coordinates of the points where the graphs of $f$ and $g$ intersect.

[3]

Sketch the graphs of $f$ and $g$ , shading the region bounded by $f$ , $g$ and the x-axis.

[3]

Find the area of the region bounded by the graphs of $f$ , $g$ , and the x-axis.

[4]

Question 4

HLPaper 1

A solid is formed by rotating the region bounded by the curve $y = ln x$ , the x-axis, and the line $x = e$ about the y-axis.

Sketch the region to be rotated.

[2]

Find the volume of the solid formed.

[5]

Question 5

SLPaper 1

Consider the function $f (x) = 4 - x^{2}$ for $- 2 \leq x \leq 2$ .

Sketch the graph of $y = f (x)$ .

[2]

Find the area enclosed by the graph of $y = f (x)$ and the x-axis.

[4]

IB Mathematics Analysis and Approaches SL 5.11—definite Integrals, Areas Under Curve Onto X-axis and Areas Between Curves Questionbank

IB Mathematics Analysis and Approaches SL 5.11—definite Integrals, Areas Under Curve Onto X-axis and Areas Between Curves Questionbank

Unlock all 34 questions with a free account

IB Mathematics Analysis and Approaches SL 5.11—definite Integrals, Areas Under Curve Onto X-axis and Areas Between Curves Questionbank

IB Mathematics Analysis and Approaches SL 5.11—definite Integrals, Areas Under Curve Onto X-axis and Areas Between Curves Questionbank

IB Mathematics Analysis and Approaches (AA) Topic SL 5.11—definite Integrals, Areas Under Curve Onto X-axis and Areas Between Curves Questionbank

Unlock all 34 questions with a free account