\(∫^5_0\,cos(π(x-[\frac{x}{2}]))dx \), where [t] denotes greatest integer less than or equal to t, is equal to
- -3
- -2
- 2
- 0
The Correct Option is D
Solution and Explanation
The correct option is(D): 0
\(∫^5_0\,cos(π(x-[\frac{x}{2}]))dx\)
\(\frac{\sin\pi{x}}{\pi}|^2_0+\frac{\sin(\pi(x-1))}{\pi}|^4_2+\frac{\sin(\pi(x-2))}{\pi}|^5_4\)
= 0 + 0 + 0 = 0
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Concepts Used:
Types of Differential Equations
There are various types of Differential Equation, such as:
Ordinary Differential Equations:
Ordinary Differential Equations is an equation that indicates the relation of having one independent variable x, and one dependent variable y, along with some of its other derivatives.
\(F(\frac{dy}{dt},y,t) = 0\)
Partial Differential Equations:
A partial differential equation is a type, in which the equation carries many unknown variables with their partial derivatives.
Linear Differential Equations:
It is the linear polynomial equation in which derivatives of different variables exist. Linear Partial Differential Equation derivatives are partial and function is dependent on the variable.
Homogeneous Differential Equations:
When the degree of f(x,y) and g(x,y) is the same, it is known to be a homogeneous differential equation.
\(\frac{dy}{dx} = \frac{a_1x + b_1y + c_1}{a_2x + b_2y + c_2}\)
Read More: Differential Equations