The branch of calculus where we get to study about integrals and their properties is known as Integral Calculus. It is a function F(a), which is an antiderivative of a function f(a) if for all in the domain of f, F’(a) = f(a).
Formula for Integral Calculus
In this page, you’ll see the basic calculus formula and the practice examples.
\(\begin{array}{l}\int f(a)da\end{array} \) = F(a) + C, where C is a constant |
Integral Calculus Examples:
Example 1: Find the integral calculus of sin(a) da?
Solution: The function
\(\begin{array}{l}\int\end{array} \)
sin(a) da has the integral -cos(a) + c , so it will be written as \(\begin{array}{l}\int\end{array} \)
sin(a) da = -cos(a) + c
Example 2: Find what is
\(\begin{array}{l}\int\end{array} \)
cos a + a d(a)
Use sum rule :
\(\begin{array}{l}\int\end{array} \)
cos a + a d(a) = \(\begin{array}{l}\int\end{array} \)
cos a da + \(\begin{array}{l}\int\end{array} \)
a d(a)
Writing the integral of each,
= sin a +
\(\begin{array}{l}\frac{a^{2}}{2}\end{array} \)
+ c
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