TS EAMCET · Maths · Area Under Curves
The area (in square unit) of the region enclosed by the curves \(y=x^2\) and \(y=x^3\) is
- A \(\frac{1}{12}\)
- B \(\frac{1}{6}\)
- C \(\frac{1}{3}\)
- D \(1\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{12}\)
Step-by-step Solution
Detailed explanation
Given curves are \(y=x^2\) and \(y=x^3\). Intersection point is \((1,1)\). \(\begin{aligned} \text { Area } & =\int_0^1\left(x^2-x^3\right) d x \\ & =\left[\frac{x^3}{3}-\frac{x^4}{4}\right]_0^1 \\ & =\frac{1}{3}-\frac{1}{4}=\frac{1}{12} \text { sq unit }\end{aligned}\)
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