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A day full of math games & activities. Find one near you.
The area of the region between the graph of y = 3x2 + 2x and the x-axis from x = 1 to x = 3 is
Solution:
Given, y = 3x2 + 2x
We have to find the area of the region between the graph y = 3x2 + 2x and the x-axis from x = 1 to x = 3.
Using integration,
Area = \(\int_{1}^{3}3x^{2}+2x\, dx \\\int x^{n}\, dx=\frac{x^{n+1}}{n+1}\)
We can use the second fundamental theorem of calculus.
\(\\Area \: =\: \left [ x^{3} +x^{2}\right ]from x=1\, to\, x=3 \\\int_{a}^{b}F(x)dx=f(b)-f(a)\)
Where, f’(x) = F(x)
Now, area = [(3)3 + (3)2] - [(1)3 + (1)2]
Area = (27 + 9) - (1 + 1)
Area = 36 - 2
Area = 34 square units
Therefore, the area of the region is 34 square units.
The area of the region between the graph of y = 3x2 + 2x and the x-axis from x = 1 to x = 3 is
Summary:
The area of the region between the graph of y = 3x2 + 2x and the x-axis from x=1 to x = 3 is 34 square units.
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