What is the indefinite integral of sinx?

The general antiderivative of sin(x) is −cos(x)+C . With an integral sign, this is written: ∫sin(x) dx=−cos(x)+C .

What functions do not have Antiderivatives?

Examples of functions with nonelementary antiderivatives include:

• (elliptic integral)
• (logarithmic integral)
• (error function, Gaussian integral)
• and (Fresnel integral)
• (sine integral, Dirichlet integral)
• (exponential integral)
• (in terms of the exponential integral)
• (in terms of the logarithmic integral)

How do you find indefinite integrals using substitution?

Substitution in the indefinite integral

1. Calculate the derivative of u, and then solve for “dx.”
2. Substitute the expression for u in the original integral, and also substitute for dx.
3. Eliminate the variable x, if it is still present, leaving an integral in u only.
4. Simplify the integrand.
5. Evaluate the simplified integral.

Are indefinite integrals derivatives?

In calculus, an antiderivative, inverse derivative, primitive function, primitive integral or indefinite integral of a function f is a differentiable function F whose derivative is equal to the original function f. Antiderivatives are often denoted by capital Roman letters such as F and G.

What is the integral of sin(x)/x from 0 to infinity?

Integral of sin (x)/x from 0 to infinity. In red: f ( x )=sin ( x )/ x; in blue: F ( x ). Today we have a tough integral: not only is this a special integral (the sine integral Si ( x )) but it also goes from 0 to infinity! Since this is a special integral, there is no elementary antiderivative and therefore we can’t simply plug the bounds into

What is f(x) = sin(x)?

In red: f ( x )=sin ( x )/ x; in blue: F ( x ). Today we have a tough integral: not only is this a special integral (the sine integral Si ( x )) but it also goes from 0 to infinity!

What is the elementary antiderivative of the sine integral?

Today we have a tough integral: not only is this a special integral (the sine integral Si ( x )) but it also goes from 0 to infinity! Since this is a special integral, there is no elementary antiderivative and therefore we can’t simply plug the bounds into the result; this means none of the techniques we know of will work.

What is the difference between indindefinite integrals and definite integrals?

Indefinite integrals are used to find the formula for the area under a curve of function f (x), whereas definite integrals allow you to calculate the value of the area. It’s like the area of a rectangle, b*h: this is the formula, and in order to find the value you have…