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Area bounded by the curves y=x^3, the x-axis and the ordinates

Question

Area bounded by the curves $y = x^{3}$ , the $x$ -axis and the ordinates $x = - 2$ and $x = 1$ is

- 9

- \frac{15}{4}

\frac{15}{4}

\frac{17}{4}

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Noah Discussed

Area bounded by the curves

y = x^{3}

, the

x

-axis and the ordinates

x = - 2

and

x = 1

10 mins ago

Discuss this question LIVE

10 mins ago

Text solutionVerified

Required area

= - \int_{- 2}^{0} x^{3} d x + \int_{0}^{1} x^{3} d x

= - [\frac{x ^{4}}{4}]_{- 2}^{0} + [\frac{x ^{4}}{4}]_{0}^{1}

= - [0 - \frac{( - 2 ) ^{4}}{4}] + \frac{1}{4}

= (\frac{1}{4} + 4) = \frac{17}{4}

sq. units
Thus, the correct answer is D.

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Question Text	Area bounded by the curves $y = x^{3}$ , the $x$ -axis and the ordinates $x = - 2$ and $x = 1$ is
Answer Type	Text solution:1
Upvotes	150