The area bounded by the curve y = x2 + 4x +5, axes of coordinates and minimum ordinate is

Question

The area bounded by the curve y = x2 + 4x +5, axes of coordinates and minimum ordinate is (A) 3(2/3) sq. units (B) 4(2/3) sq. units (C) 5(2/3) sq. units (D) none of these

Tardigrade Admin · Accepted Answer

y = x2 + 4x+5 = (x + 2)2+1 <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/a121f04a49db4eb8bc7b961a8bf9e2b0-.png" /> A=∫ limits-20(x2+4x+5)dx=[(x3/3)+2x2+5x]-20 =-[-(8/3)+8-10]=2+(8/3)=(14/3)=4(2/3) sq. units

Q. The area bounded by the curve $y = x^{2} + 4 x + 5$ , axes of coordinates and minimum ordinate is

$3 \frac{2}{3}$ sq. units

$4 \frac{2}{3}$ sq. units

$5 \frac{2}{3}$ sq. units

none of these

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

$A = - 2 \int 0 (x^{2} + 4 x + 5) d x = [\frac{x ^{3}}{3} + 2 x^{2} + 5 x]_{- 2}^{0}$

$= - [- \frac{8}{3} + 8 - 10] = 2 + \frac{8}{3} = \frac{14}{3} = 4 \frac{2}{3}$ sq. units

Q. The area bounded by the curve y=x2+4x+5, axes of coordinates and minimum ordinate is

332​ sq. units

432​ sq. units

532​ sq. units