Question
Question: \(\int _ { - 1 } ^ { 1 } x | x | d x =\)...
∫−11x∣x∣dx=
A
1
B
0
C
2
D
Answer
0
Explanation
Solution
Let f(x)=x∣x∣. Then f(−x)=−x∣−x∣=−x∣x∣=−f(x)
Therefore∫−11x∣x∣dx=0,
(By the property of definite integral).
∫−11x∣x∣dx=
1
0
2
0
Let f(x)=x∣x∣. Then f(−x)=−x∣−x∣=−x∣x∣=−f(x)
Therefore∫−11x∣x∣dx=0,
(By the property of definite integral).