Definite integral

Everything You Need in One Place

Homework problems? Exam preparation? Trying to grasp a concept or just brushing up the basics? Our extensive help & practice library have got you covered.

Learn and Practice With Ease

Our proven video lessons ease you through problems quickly, and you get tonnes of friendly practice on questions that trip students up on tests and finals.

Instant and Unlimited Help

Our personalized learning platform enables you to instantly find the exact walkthrough to your specific type of question. Activate unlimited help now!

Get the most by viewing this topic in your current grade. Pick your course now.

?
Examples
Lessons
  1. Use the graph of ff to evaluate each integral by interpreting it in terms of areas.
    Definite integral
    1. ∫−11f(x)dx \int_{-1}^{1} f(x)dx
    2. ∫12f(x)dx \int_{1}^{2} f(x)dx
    3. ∫24f(x)dx \int_{2}^{4} f(x)dx
    4. ∫48f(x)dx\int_{4}^{8} f(x)dx
    5. ∫89f(x)dx\int_{8}^{9} f(x)dx
    6. ∫−19f(x)dx \int_{-1}^{9} f(x)dx
  2. Evaluate the integral by interpreting it in terms of areas.
    1. ∫02(2−2x)dx\int_{0}^{2}(2-2x)dx
    2. ∫024−x2dx\int_{0}^{2}\sqrt{4-x^2}dx
    3. ∫−21∣x∣dx \int_{-2}^{1}|x|dx
  3. if ∫310f(x)dx=15\int_{3}^{10}f(x)dx=15 and ∫38f(x)dx=9\int_{3}^{8}f(x)dx=9, find ∫810f(x)dx\int_{8}^{10}f(x)dx
    Topic Notes
    ?
    In this section, we will evaluate definite integrals by calculating the area under the curve. We see that the region of integration depends on the lower limit and upper limit of the integral. These areas will be fairly easy to calculate since most of the areas under the curve involve shapes that are familiar to us. We will also notice that curves under the x-axis gives us negative area. Next, we will take a look at questions which involves sketching the curve ourselves, and then determining the area. Lastly, we will take a look at a unique question which involves finding the area of a specific region when given information about two definite integrals.
    Definite integral
    ∫abf(x)dx= \int_{a}^{b} f(x) dx = area under the curve from aa to bb
    Basic Concepts
    ?
    Related Concepts
    ?