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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Area Under Curves

NTA Abhyas 2020 · Mathematics · Area Under Curves

A farmer F _ 1 has a land in the shape of a triangle with vertices...

A farmer F1{F}_{1} has a land in the shape of a triangle with vertices at P(0,0),Q(1,1)P ( 0, 0 ) , Q ( 1, 1 ) and R(2,0).R ( 2, 0 ) . From this land, a neighbouring farmer F2{F}_{2} takes away the region which lies between the side PQPQ and a curve of the form y=xn;(n>1).y = {x}^{n}; ( n > 1 ) . If the area of the region taken away by the farmer F2{F}_{2} is exactly 3030% of the area of ∆PQR,∆ PQR, then the value of nn isA farmer F _ 1 has a land in the shape of a triangle with vertices at P ( 0, 0 ) , Q ( 1, 1 ) and R ( 2, 0 ) . From

Correct answer

4

Step-by-step solution

A farmer F _ 1 has a land in the shape of a triangle with vertices at P ( 0, 0 ) , Q ( 1, 1 ) and R ( 2, 0 ) . From

Area =∫01(x−xn)dx=310= \mathop{∫}_{0}^{1}\left(x - {x}^{n}\right)dx = \dfrac{3}{10}

[x22−xn+1n+1]01=310{\left[\dfrac{{x}^{2}}{2} - \dfrac{{x}^{n + 1}}{n + 1}\right]}_{0}^{1} = \dfrac{3}{10}

12−1n+1=310\dfrac{1}{2} - \dfrac{1}{n + 1} = \dfrac{3}{10} ∴n+1=5∴ n + 1 = 5

⇒n=4⇒ n = 4
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