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वक्र `y =x^(3)`, X-अक्ष एव कोटियों `x = -2, x =1` से घिरे का क्षेत्रफल से घिरे क्षेत्र क्षेत्रफल है :
A. ` -9`
B. `(-15)/(4)`
C. `(15)/(4)`
D. `(17)/(4)`

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दिया गया वक्र है
` y = x^(3)` .
`x = - x` तथा `y = -y` रखने पर ` y= x^(3)` प्राप्त है । अतः वक्र विपरीत चतुर्थेाश में सममित है तथा मुल -बिन्दु (0,0) से होकर जाता है।
image
`therefore` अभीष्ट क्षेत्रफल `= int_(-2)^(1) |x^(3)| dx`
` = int_(-2)^(0)|x^(3)|dx + int_(0)^(1) | x^(3)| dx`
` = int_(-2)^(0)(-x^(3))dx+int_(0)^(1)dx`
`= - [(x^(4))/(4)]_(-2)^(0) + [(x^(4))/(4)]_(0)^(1)`
` = - [0-((-2)^(4))/(4)]+[(1)/(4)-0]`
` = - (-4) +((1)/(4)) = (17)/(4)`वर्ग इकाई

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