Question

The area bounded by the curve $ y = \cos x $, $ x = 0 $, and $ x = \pi $ is

• A. 2 sq units
• B. 1 sq units
• C. 4 sq units
• D. 3 sq units

Hint:

When calculating the area under a curve, make sure to set up the definite integral correctly and evaluate it at the proper limits.

Answer 1

The Correct Option is A

The area under the curve \( y = \cos x \) from \( x = 0 \) to \( x = \pi \) is given by the integral: \[ A = \int_0^\pi \cos x \, dx \] The integral of \( \cos x \) is \( \sin x \), so: \[ A = \left[ \sin x \right]_0^\pi = \sin \pi - \sin 0 = 0 - 0 = 2 \] Thus, the area is 2 square units.