Fiind the area between the curve y=tan x and the x-axis

Question

from x=-pi/4 to pi/3?

Answer 1

Given the curve y = tan(x) and the x - axis i.e. y = 0.

The area is A =  ʃ[tan(x) - 0]dx = ʃ tan(x)dx

ʃ tan(x)dx from x=-pi/4 to pi/3

Trigonometric functions: ʃ tan(x)dx = - log|cos(x)|+C

Therefore The area is 0.1505.

Comments

The area between the curve y = tan(x) and the x - axis from x = -pi/4 to pi/3 is 1.0397 squre units.

Answer 2

Given the curve y = tan(x) and the x - axis i.e. y = 0.

The area is A =  ʃ[tan(x) - 0]dx = ʃ tan(x)dx

To find the area, just integrate the given curve on .

Trigonometric functions: ʃ tan(x)dx = - log|cos(x)|+C

Therefore the area is 1.0397 squre units.