How to calculate points using excel

There are two main ways to perform integral calculations in Excel: 1. Using the INTEGRAL function; 2. Using numerical integration methods (trapezoidal or Simpson's method).

How to perform integral calculation in Excel

There are two main ways to perform integral calculation in Excel:

1. Use the INTEGRAL function

INTEGRAL function can directly calculate the definite integral. The syntax is:

<code>=INTEGRAL(cell, x_variable, lower_limit, upper_limit)</code>

where:

• cell: contains the cell reference of the integrated function
• x_variable : Cell reference of the integration variable
• lower_limit : Cell reference of the lower limit of the integration
• upper_limit : Cell reference of the upper limit of the integration

Example:

Calculate the function sin(x) on the interval [0, π/2] Integration:

<code>=INTEGRAL(SIN(A1), A1, 0, PI()/2)</code>

2. Use numerical integration method

When the integral function is complex or cannot be solved analytically, you can use numerical integration method, such as trapezoidal method or Simpson Law.

Trapezoidal method:

Divide the integration interval into n sub-intervals, and the width of each sub-interval is h. The integral value is approximately:

<code>∫[a, b] f(x) dx ≈ h/2 * [f(a) + 2f(a+h) + 2f(a+2h) + ... + 2f(b-h) + f(b)]</code>

In Excel, you can use the following formula to calculate the trapezoidal method integral:

<code>=H() * (F(A1) + SUMPRODUCT(2, F(A2:A10)) + F(A11)) / 2</code>

Simpson’s method:

Simpson’s method ratio The trapezoidal method is more accurate, and its integral value is approximately:

<code>∫[a, b] f(x) dx ≈ h/3 * [f(a) + 4f(a+h) + 2f(a+2h) + 4f(a+3h) + ... + 2f(b-2h) + 4f(b-h) + f(b)]</code>

In Excel, you can use the following formula to calculate the Simpson method integral:

<code>=H() * (F(A1) + 4*F(A3:A9:A10) + 2*F(A2:A4:A8:A10) + F(A11)) / 3</code>

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