The value of ∫-23|1-x2| dx is

Question

The value of ∫-23|1-x2| dx is (A)  (7/3)  (B)  (14/3)  (C)  (28/3)  (D)  (1/3)

Tardigrade Admin · Accepted Answer

∫-23|1-x2|dx =∫-2-1(x2-1)dx+∫-11(1-x2)dx +∫13(x2-1)dx =[ (x3/3)-x ]-2-1+[ x-(x3/3) ]-11+[ (x3/3)-x ]13 =(2/3)+(2/3)+2( (2/3) )+(9-3)-( (1/3)-1 ) =(28/3)

Q. The value of $\int_{- 2}^{3} ∣1 - x^{2} ∣ d x$ is

$\frac{7}{3}$

$\frac{14}{3}$

$\frac{28}{3}$

$\frac{1}{3}$

Q. The value of ∫−23​∣1−x2∣dx is

37​

314​

328​

31​

∫−23​∣1−x2∣dx =∫−2−1​(x2−1)dx+∫−11​(1−x2)dx +∫13​(x2−1)dx =[3x3​−x]−2−1​+[x−3x3​]−11​+[3x3​−x]13​ =32​+32​+2(32​)+(9−3)−(31​−1) =328​

Q. The value of $\int_{- 2}^{3} ∣1 - x^{2} ∣ d x$ is

$\frac{7}{3}$

$\frac{14}{3}$

$\frac{28}{3}$

$\frac{1}{3}$