Evaluate the integral of (x dx) / (x^2 + 2) with lower limit of 0 and upper limit of 1
Problem
Evaluate $\displaystyle \int_0^1 \dfrac{x \, dx}{x^2 + 2}$.
| A. 0.2027 | C. 0.2270 |
| B. 0.2207 | D. 0.2072 |
limits of integration
Example 6 | Plane Areas in Rectangular Coordinates
Example 6
Find each of the two areas bounded by the curves y = x3 - 4x and y = x2 + 2x.
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Example 3 | Plane Areas in Rectangular Coordinates
Example 3
Find the area bounded by the curve x = y2 + 2y and the line x = 3.
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Example 2 | Plane Areas in Rectangular Coordinates
Example 2
Find the area bounded by the curve a2 y = x3, the x-axis and the line x = 2a.
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Example 1 | Plane Areas in Rectangular Coordinates
Example 1
Find the area bounded by the curve y = 9 - x2 and the x-axis.
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Plane Areas in Rectangular Coordinates | Applications of Integration
There are two methods for finding the area bounded by curves in rectangular coordinates. These are...
- by using a horizontal element (called strip) of area, and
- by using a vertical strip of area.
The strip is in the form of a rectangle with area equal to length × width, with width equal to the differential element. To find the total area enclosed by specified curves, it is necessary to sum up a series of rectangles defined by the strip.