Exercises for Question Type 4: Calculating the area between any function in the positive section and the x axis (using technology)

Loading subject…

Exercises for Question Type 4: Calculating the area between any function in the positive section and the x axis (using technology) - IB

Question 1

The question asks for the evaluation of a definite integral representing an area under a curve using a graphing calculator.

Using a graphing calculator, determine the area under f (x) = e^{- x} cos (x) from x = 0 to x = \frac{π}{2} .

[3]

Question 2

This question assesses the ability to set up and evaluate a definite integral representing the area under a curve using technology (GDC).

Calculate, using technology, the area under f (x) = \frac{1}{x ^{2} + 1} above the x -axis from x = 0 to x = 1 .

[2]

Question 3

Using technology, find the area between f (x) = e^{x} ln (2 x) and the x -axis from x = 0.5 to x = 1 .

[2]

Question 4

Find the area under f (x) = x ln (x) from x = 1 to x = e using a graphing calculator.

[2]

Question 5

Calculate the area under the curve f (x) = x^{2} above the x -axis between x = 0 and x = 2 using technology.

[2]

Question 6

Using technology, compute the area under f (x) = ln (x + 1) above the x -axis between x = 0 and x = 2 .

[3]

Question 7

Calculate the area between f (x) = x e^{x} and the x -axis on the interval [1, 3] using technology.

[3]

Question 8

Determine the area under the curve f (x) = 4 - x^{2} from x = 0 to x = 2 using a graphing calculator.

[2]

Question 9

Determine the area under f (x) = sin (x^{2}) above the x -axis between x = 0 and x = π using technology.

[2]

Question 10

Using a graphing calculator, compute the area under f (x) = arctan (x) from x = 0 to x = 1 .

[2]

Question 11

Finding the area under a curve using a graphing calculator.

Find the area between f (x) = e^{x} and the x -axis from x = 0 to x = 1 using a graphing calculator.

[2]

Question 12

Calculate, with technology, the area under the curve f (x) = x e^{- x^{2}} above the x -axis between x = 0 and x = 1 .

[2]

IB Mathematics Applications & Interpretation Question Type 4: Calculating the Area Between Any Function in the Positive Section and the x Axis Exercises