Integral of Sin x From 0 to π
To find the integral of sin(x) from 0 to π, we can use the antiderivative. The antiderivative of sin(x) is -cos(x). Evaluating this antiderivative from 0 to π, we get:
∫0πsin(x) dx = [-cos(π) – (-cos(0))]
∫0πsin(x) dx = [-(-1) + 1]
Since cos(π) is -1 and cos(0) is 1, the expression simplifies to:
∫0πsin(x) dx = 1 + 1 = 2
So, the integral of sin(x) from 0 to π is equal to 2. This represents the signed area between the sin(x) curve and the x-axis from x = 0 to x = π.
Integral of Sin x
Integral of sin x is -cos(x) plus a constant (C). It represents the area under the sine curve. The function repeats every 2π radians due to its periodic nature. This article explains the integral of the sine function, showing its formula, proof, and application in finding specific definite integrals. Further, it mentions solved problems and frequently asked questions.
Table of Content
- What is Integral of Sin x?
- Integral of Sin x Formula
- Graphical Significance of Integral of Sin x
- Integral of Sin x Proof by Substitution Method
- Definite Integral of Sin x
- Integral of Sin x From 0 to π
- Integral of Sin x From 0 to π/2