TS EAMCET · Maths · Area Under Curves
The area bounded by \(y=x^2+2, x\)-axis, \(x=1\) and \(x=2\) is
- A \(\frac{16}{3}\) sq unit
- B \(\frac{17}{3}\) sq unit
- C \(\frac{13}{3}\) sq unit
- D \(\frac{20}{3}\) sq unit
Answer & Solution
Correct Answer
(C) \(\frac{13}{3}\) sq unit
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { Required area }=\text { Area of curve } A B C D \\ & \quad=\int_1^2 y d x=\int_1^2\left(x^2+2\right) d x=\left[\frac{x^3}{3}+2 x\right]_1^2 \\ & \quad=\left(\frac{8}{3}+4\right)-\left(\frac{1}{3}+2\right)=\frac{20}{3}-\frac{7}{3}=\frac{13}{3} \text { sq…
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