What is integral of cos 5x?

Explanation : =∫(cos5x)dx. From trigonometric identity, which is. cos2x+sin2x=1 , ⇒cos2x=1−sin2x.

What is the integration of cos x dx?

The integral of cos x dx is sin x. Mathematically, this is written as ∫ cos x dx = sin x + C, where, C is the integration constant.

What is the integration of sin theta?

The integral of sin x is -cos x. Mathematically, this is written as ∫ sin x dx = -cos x + C, were, C is the integration constant.

What is the integration of Cos?

The Fundamental Theorem of Calculus

Function	Integral
cos(x)	sin(x) + C
-sin(x)	cos(x) + C
sec 2 (x)	tan(x) + C
-csc(x)cot(x)	csc(x) + C

What is the integration of Cos X with respect to X?

Calculus Examples The integral of cos(x) with respect to x is sin(x) .

What is the integration of Cos 2x?

Solution. The integral of cos(2x) is (1/2)sin(2x) + C, where C is a constant.

What is the value of ∫π 0 sin (x) dx?

This means ∫π 0 sin(x)dx= (−cos(π))−(−cos(0)) =2 ∫ 0 π sin ( x) d x = ( − c o s ( π)) − ( − c o s ( 0)) = 2. Sometimes an approximation to a definite integral is desired.

What is the derivative of-cos (x)?

For example,∫ sin(x)dx= −cos(x)+constant ∫ s i n ( x) d x = − c o s ( x) + c o n s t a n t, since the derivative of −cos(x)+constant − c o s ( x) + c o n s t a n t is sin(x) s i n ( x).

What is integral integration in calculus?

Integration is an important tool in calculus that can give an antiderivative or represent area under a curve. The indefinite integral of f (x) f (x), denoted ∫ f (x)dx ∫ f (x) d x, is defined to be the antiderivative of f (x) f (x). In other words, the derivative of ∫ f (x)dx ∫ f (x) d x is f (x) f (x).

What is the definite integral of f (x)?

The definite integral of f (x) f ( x) from x = a x = a to x = b x = b, denoted ∫b a f (x)dx ∫ a b f ( x) d x, is defined to be the signed area between f (x) f ( x) and the x x axis, from x= a x = a to x= b x = b. Both types of integrals are tied together by the fundamental theorem of calculus.