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)