The antiderivative of Sinx is cos (x) +C. With the use of the integral sign, this particular variant can be written as:
∫sin(x) dx= -cos(x) +C
The anti-derivative for any function, represented by f(x), is the
same as the function's integral. This simply translates to the
This means the resulting value for sin (x) shall be:
This particular value is the common integral for:
∫sin(x) dx = -cos(x)+C
Integration or antiderivative is something that can effectively be used for finding the volume, area, center points, as well as many other useful things. However, it is mostly used for finding the overall area below the function graph or integral of Sin (X).
When calculating Sin X antiderivative, one can use the power method. This integration formula is actually the inverse for power rule that can be used in the differentiation calculation. This gives us indefinite integral for the variable which is raised to power.
Constant Coefficient Rule:
Also known as the constant multiplier method, this process basically tells that indefinite integral for c.f(x) equals indefinite integral for f(x) which can be multiplied with use of c. Here f(x) is the function & c represents constant coefficient.
When wondering about the possible integration methods for Sin X, Integration's sum method notes that we need to integrate the functions which is the summation of multiple terms. Basically, it states that each term needs to be integrated separately and then added together.
For calculation of integrals, it is important to understand the difference method. It tells the way to integrate functions which involve noting difference between terms more than two. Essentially, the rule is same as Sum Rule but the final terms and integrated separately.