Home » If (y = x(x^4 + x + 1)), evaluate (int limits_{0} ^{1} y mathrm d x).

If (y = x(x^4 + x + 1)), evaluate (int limits_{0} ^{1} y mathrm d x).

If (y = x(x^4 + x + 1)), evaluate (int limits_{0} ^{1} y mathrm d x).

  • A.
    (frac{11}{12})
  • B.
    1
  • C.
    (frac{5}{6})
  • D.
    zero
Correct Answer: Option B
Explanation

(y = x(x^{4} + x + 1) = x^{5} + x^{2} + x)

(int limits_{0} ^{1} (x^{5} + x^{2} + x) mathrm d x = frac{x^{6}}{6} + frac{x^{3}}{3} + frac{x^{2}}{2})

= ([frac{x^{6}}{6} + frac{x^{3}}{3} + frac{x^{2}}{2}]_{0} ^{1})

= (frac{1}{6} + frac{1}{3} + frac{1}{2})

= (1)

Related:  Mathematics Theory (a) In the diagram, O is the centre of the circle radius 3.2cm. If