The area bounded by the curve y=2 x4-x2, x-axis and the two ordinates corresponding to the minima of the function is

Question

The area bounded by the curve y=2 x4-x2, x-axis and the two ordinates corresponding to the minima of the function is (A) (3/120) (B) (5/120) (C) (1/20) (D) (7/120)

Tardigrade Admin · Accepted Answer

(d y/d x)=8 x3-2 x, (d y/d x) =0 ⇒ (4 x2-1) x=0 <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/663c0558af1025a29955ffd9c24707bb-.png" /> ⇒ x=-(1/2), 0, (1/2) Required area =-2 ∫ limits01 / 2(2 x4-x2) d x=(7/120)

Q. The area bounded by the curve $y = 2 x^{4} - x^{2}, x$ -axis and the two ordinates corresponding to the minima of the function is

$\frac{3}{120}$

$\frac{5}{120}$

$\frac{1}{20}$

$\frac{7}{120}$

$\frac{d y}{d x} = 8 x^{3} - 2 x, \frac{d y}{d x} = 0 \Rightarrow (4 x^{2} - 1) x = 0$

$\Rightarrow x = - \frac{1}{2}, 0, \frac{1}{2}$
Required area $= - 2 0 \int 1/2 (2 x^{4} - x^{2}) d x = \frac{7}{120}$

Q. The area bounded by the curve y=2x4−x2,x-axis and the two ordinates corresponding to the minima of the function is

1203​

1205​

201​

1207​