Numerical integration (integral, trapz) in MATLAB - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to calculate the integral of sin(x) from 0 to pi using the integral function.

MATLAB

result = integral(@(x) sin(x), 0, [1]);

Drag options to blanks, or click blank then click option'

Api

B2*pi

C0

Dpi/2

Attempts:

3 left

💡 Hint

Common Mistakes

Using 2*pi as the upper limit instead of pi.

Setting the upper limit to 0 which results in zero area.

The integral of sin(x) from 0 to pi is calculated by setting the upper limit to pi.

2fill in blank

medium

Complete the code to approximate the integral of cos(x) from 0 to pi using the trapz function with 100 points.

MATLAB

x = linspace(0, pi, 100);
y = cos(x);
result = trapz(x, [1]);

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Acos(x).^2

Bx

Cy

Dsin(x)

Attempts:

3 left

💡 Hint

Common Mistakes

Passing x instead of y to trapz.

Passing an unrelated function like sin(x).

The trapz function integrates the values in y over x. So we pass y as the second argument.

3fill in blank

hard

Fix the error in the code to correctly compute the integral of exp(-x^2) from -1 to 1 using integral.

MATLAB

result = integral(@(x) exp(-[1].^2), -1, 1);

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AX

Bt

Cy

Dx

Attempts:

3 left

💡 Hint

Common Mistakes

Using uppercase X instead of lowercase x.

Using a different variable name like t or y.

The anonymous function uses x as the input variable, so the variable inside the function must be x.

4fill in blank

hard

Fill both blanks to create a vector of squares for x from 1 to 5, including only values greater than 4, using logical indexing. This can be useful for selecting weights or points in numerical integration.

MATLAB

x = 1:5;
values = x(x [2] 4).[1]2;

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A.^

B>

C<

D*

Attempts:

3 left

💡 Hint

Common Mistakes

Using * instead of .^ for element-wise power.

Using < instead of > in the condition.

Use .^ for element-wise power and > to filter values greater than 4.

5fill in blank

hard

Fill all three blanks to create a structure with fields as uppercase letters of x, values as y, and filter y values greater than 0.5. This can store selected significant function values for numerical integration points.

MATLAB

result = struct();
for i = 1:length(x)
    if y(i) [1] 0.5
        field = upper([2](i));
        result.(field) = [3](i);
    end
end

Drag options to blanks, or click blank then click option'

A>

Bx

Cy

D<

Attempts:

3 left

💡 Hint

Common Mistakes

Using < instead of > in the condition.

Using y instead of x for the field name.

Assigning x(i) instead of y(i) as the value.

The condition checks if y(i) is greater than 0.5, the field name is uppercase of x(i), and the value assigned is y(i).