Evaluate the integral by interpreting it in terms of areas.
{eq}\displaystyle \int_{-3}^4 |x|\ dx {/eq}.
Question:
Evaluate the integral by interpreting it in terms of areas.
{eq}\displaystyle \int_{-3}^4 |x|\ dx {/eq}.
Interpretation of Riemann Integration in Terms of Area :
Suppose {eq}f:[a,b]\to \mathbb{R} {/eq} is a continuous function. Also suppose that {eq}f(x)>0 {/eq} for all {eq}x {/eq} in {eq}[a,b]. {/eq} Then {eq}\displaystyle\int_{a}^{b}f(x)\ dx {/eq} can be interpreted as the area enclose by the lines {eq}x=a {/eq}, {eq}x=b, y=0 {/eq} and the curve {eq}y=f(x). {/eq}
Answer and Explanation: 1
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View this answerSo, {eq}\displaystyle \int_{-3}^4 |x|\ dx {/eq}
=The area enclosed by the lines {eq}x=-3,x=4,y=0 {/eq} and the curve {eq}y=|x|. {/eq}
=The area...
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Chapter 12 / Lesson 5The area, or Riemann sum, is contained by boundaries, known as limits, that can be calculated. Learn about the concept of Riemann sums, where they are used, and how the limits and integrals can be defined mathematically.