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Definite integralsCalculusCollegeabout 0:44

Definite integral of 3 from -2 to 5: animated lesson

A narrated, step-by-step definite integrals video lesson with captions. Final answer: 21.

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Video with a synthetic English voice and captions. Pick another language for subtitles in that language, or open the interactive version.

Video narrated by a synthetic voice (Piper TTS, en_US-ljspeech-high voice (LJ Speech dataset, public domain)); the steps come from our maths engine and the answer was checked independently. Download MP4 (0.3 MB) · Captions (WebVTT)

Steps on screen

1. The problem
Evaluating an integral
$\int_{-2}^{5} 3\,dx$
2. Step by step
1. $\int_{-2}^{5} 3\,dx$
  Start with the definite integral
2. $\int 3\,dx = 3x$
  Constant rule: ∫ k dx = kx
3. $F(x) = 3x$
  Antiderivative
4. $F(5) - F(-2) = 15 - \left(-6\right) = 21$
  Apply the fundamental theorem of calculus
3. The answer
$\int_{-2}^{5} 3\,dx = 21$
∫ from -2 to 5 = 21
4. Check
- Differentiated the antiderivative and compared it with the integrand ✓
- Adaptive Simpson's rule gives 21 ✓

Transcript

The problem. Here is the problem: integral of 3 from negative 2 to 5. Evaluate the definite integral of 3 from x equals negative 2 to x equals 5.

Step by step. Start with the definite integral. Constant rule: the integral of k dx equals kx. Antiderivative. Apply the fundamental theorem of calculus.

The answer. So the answer is 21. A definite integral gives the signed area between the curve and the x-axis: area above the axis counts as positive and area below counts as negative.

Check. Differentiated the antiderivative and compared it with the integrand, which checks out. Adaptive Simpson prime s rule gives 21, which checks out.

About definite integrals

Evaluate definite integrals with the fundamental theorem of calculus.

Definite integral of 3 from -2 to 5: Step-by-Step Lesson