How to check if the integral of a function is correct with a scientific calculator? Let’s find out in this short article!
Integral is said to be a function describing the area under the curve for the given integral. Taking the integral of the derivative of the function will generate the original function. It also specifies the position of an object or solid from any given point in time based on at least two points of an object’s velocity. The manual calculation of integrals is fundamental and difficult to do, just try an Integrals Calculator that allows you to solve the integrals of the function based on the variable involved. It also shows the detailed procedure of the calculations.
How to check the correctness of the function:
If you want to calculate the integral of the function, you are solving for the anti-derivative of the function. To check whether the calculation is accurate or not, simply enter the answer into any scientific calculator using the d / dx function and then compare the results.
For example: suppose you are solving the integral of a function “cos (2x)” and the answer for this function may be sin (2x) / 2 + c but you are not so sure of the answer. All you have to do is calculate the original cos (2x) using the arbitrary substitution for “x”. then, put the cos (2 x 7) which is ~ 0.136737.
Now, you need to use the d / dx function from the calculator using the same value as x, d / dx (sin_2x) / 2), x = 7. Then, the calculator outputs the output of ~ 0.136737. If the result for the function is the same as the manually calculated result, it means you did it successfully. You can also use the integration calculator which helps you evaluate the integrals of the function and shows you the step by step procedure of the calculations.
How the scientific calculator performs integral calculations:
The scientific calculator can only calculate the definite integrals because they use approximate methods to find the value. The mathematical rule is known as “Simpson’s rule”. Simpson’s original rule is applied to the f (x) function, when the curve is smooth within the range of “a” and “b”. Often, a composite rule is applied to find the integral of a curve that is not smooth. The rationale behind using Simpson’s composite rule is to decompose the interval of “a” and “b” into smaller sub intervals. Hence, this makes the curve appear smoother in the subdivision ranges.
Suppose we divide the intervals of “a” and “b” into n subdivisions. So, you can say that by increasing the number of subdivisions we can reduce the approximation error. These calculators can solve integrals using the highest values for the variable n. You can consider the definite integral calculator to perform the computation of definite integrals. And you can use the indefinite integral calculator for indefinite integral calculations.
Why are double integrals used:
The double integral of the function is said to be a way to integrate on the two-dimensional area. Basically it is used to determine the volume of the surface that is under the curve. They have two variables that define f (x, y) in three-dimensional space.
In this article, we have discussed how to check whether the integral of a function is correct or not with the assistance of a scientific calculator. It is difficult to check the result of the integral on paper but you can do it using the calculator. It is also possible to verify the correctness of the integrals by performing the calculations on the integral calculator which shows the step-by-step procedure of the calculations.