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प्रश्न
Find the area bounded under the curve y = 3x2 + 6x + 7 and the X-axis with the ordinates at x = 5 and x = 10.
उत्तर
The given equation of the curve is y = 3x2 + 6x + 7.
The area bounded by the curve and the X-axis with coordinates x1 = 5 and x2 = 10 is given by
\[\int_{x_1}^{x_2} y dx\]
\[ = \int_5^{10} \left( 3 x^2 + 6x + 7 \right)dx\]
\[ = \left[ \frac{3 x^3}{3} + \frac{6 x^2}{2} + 7x \right]_5^{10} \]
\[ = 1000 - 125 + 300 - 75 + 70 - 35\]
\[ = 1370 - 235\]
= 1135 sq. units
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