How to check if the integral of a function is correct with a scientific calculator?
Integral is said to be a function that describes the area under the curve for the given integral. By 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 point in the given time based on at least two points of the velocity of an object. Manual calculation of integrals is critical & difficult to do so, simply give a try to an online integral calculator that allows you to solve the integrals of the function according to the variable involved. It also shows you the step-by-step procedure of the calculations.
How to check the correctness of the function:
If you want to compute the integral of the function, you’re solving for the anti-derivative of the function. To check whether the calculation is accurate or not you just need to plug in the answer in any scientific calculator by using the d / dx function and then compare the results which fits your mind and psychology better.
For instance: let’s suppose that you’re 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 about the answer. All you need to do is to calculate the original cos(2x) by using the arbitrary substitution for “x”. so, put the cos(2 x 7) that makes ~0.136737.
Now, you need to use the d/dx function from your calculator by using the same value of x, d/dx (sin_2x)/2), x = 7. So, your calculator generates the output of ~0.136737. If the result for the function is the same to the manually calculated result, then it means you did it successfully. You can also use the integration calculator that helps you to evaluate the integrals of the function and show you the step by step procedure of the calculations even in Psychology.
How scientific calculator do the integral calculations:
The scientific calculator can only calculate the definite integrals because they use the approximate methods to find the value. The mathematical rule is known as “Simpson’s rule”. The original Simpson’s Rule is applied on the function f(x), when the curve is smooth within the interval of “a” and “b”. Often, a composite rule is applied in order to find the integral of a curve that is not smooth.The basic logic of using the composite Simpson’s rule is to break down the interval of “a” and “b” into smaller sub intervals. So, in this way the curve looks smoother in the sub division intervals.
Suppose that we divide the intervals of “a” and “b” into n sub divisions. So, you can say that by increasing the number of sub divisions we can reduce the error of approximation. These calculators can solve the integrals by using the higher values for the n variable. You can consider the definite integral calculator to perform the calculation of definite integrals. And you can use the indefinite integral calculator for the indefinite integral calculations.
Why double integrals are used:
The double integral of the function is said to be a way to integrate over the two-dimensional area. It is basically used to determine the volume of the surface that is under the curve. They have two variables that define the f(x, y) in the three-dimensional space.
In this article, we 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 the paper but you can do this by using the calculator. You can also make sure of the correctness of integrals by performing the calculations on the integral calculator that shows the step by step procedure of the calculations.