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Worked solution

Evaluate an integral on the graphing calculator

Evaluate ∫023(1+x2) dx\int_0^2 3(1+x^2)\,dx.

CJC · Lecture · Example 6

Enter the template

On the source calculator home screen, press MATH then 9, or ALPHA then WINDOW then 4, to insert the definite-integral template. Enter lower limit 00, upper limit 22, integrand 3(1+x2)3(1+x^2) and variable xx; then press ENTER.

How did this part go?

Read and verify

The source display gives 1414, so ∫023(1+x2) dx=14\int_0^23(1+x^2)\,dx=14. An independent exact check is [3x+x3]02=6+8=14[3x+x^3]_0^2=6+8=14.

How did this part go?

Compare your sketch

Evaluate a definite integral

  1. 1. Insert the integral template

    On the home screen, press MATH then 9, or ALPHA then WINDOW then 4.

  2. 2. Complete all four fields

    Enter both limits, the whole integrand and the integration variable.

    Lower limit
    0
    Upper limit
    2
    Integrand
    3(1 + x²)
    Variable
    x

  3. 3. Evaluate, then check the mathematics

    Press ENTER. The retained source screen gives 14. An independent exact check is [3x + x³] from 0 to 2 = 14.

    Integral from 0 to 2 of 3(1 + x²) dx = 14

Check whether the question requires an exact result or working without a calculator. A numerical evaluation can check your answer; it does not replace a requested exact derivation.

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Reconstructed source calculator screens: empty definite-integral template, then integral from zero to two of 3(1+x squared) dx and result 14.
Reconstructed source calculator screens: empty definite-integral template, then integral from zero to two of 3(1+x squared) dx and result 14.
Reconstructed source calculator screens: empty definite-integral template, then integral from zero to two of 3(1+x squared) dx and result 14.
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Common mistakes

The displayed result depends on entering the whole integrand and both limits correctly; keep parentheses around 1+x squared.

Read the hint