Integral of Cos x Graphical Significance
We know that the integration gives the idea about the area under the curve. Hence, the integral of cos x also gives the area under the cosine curve within a defined range. The area under the cosine curve is shown below:
Area under Cosine Curve from 0 to π/2
Approximate calculation of Area under cosine curve is given as
Area of Triangle = 1/2 × b × h = 1/2 × π/2 × 1 = π/4 ≈ 0.8
Area under cosine curve from 0 to π/2 using integration is given as:
Area = ∫π/20cos xdx = [sin x] π/20
= sin π/2 – sin 0
= 1 – 0
= 1
Area under Cosine Curve from 0 to π
Approximate calculation of Area under Cosine Curve is given as:
Area of Triangle 1 + Area of Triangle 2 = (1/2 × π/2 × 1) – (1/2 × π/2 × 1) = 0
Area under Cosine curve using Integration is given as:
Area = ∫π0cos xdx = [sin x] π0
= sin π – sin 0
= 0 – 0
= 0
Hence, we verified that the integration of cos x gives the area under the cosine curve under the defined limits
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Integral of Cos x
Integral of Cos x is equal to Sin x + C. Integral of a function is the process of finding the area under the curve. Integration of Cos x gives the area of the region covered by the cosine trigonometric function. The integral also called the Antiderivative of a function, exists when the function is differentiable. Integration of Cos x is possible as the cosine function is also differentiable in its domain.
In this article, we will learn what is Integral of cos x, the formula of the Integral of cos x, and how to integrate cos x.
Table of Content
- What is Integral of Cos x?
- Integral of Cos x Formula
- Integral of cos x Formula Proof
- Definite Integral of cos x
- Integral of Cos x – Graphical Significance