NIMCET 2010 — Mathematics PYQ
NIMCET | Mathematics | 2010If ∫12−10f(x)dx=6, ∫100−10f(x)dx=−2, and ∫100−5f(x)dx=4, then ∫−512f(x)dx=?
Choose the correct answer:
- A.
0
- B.
−12
(Correct Answer) - C.
4
- D.
−2
−12
Explanation
Solving:
We use the property ∫abf(x)dx=∫acf(x)dx+∫cbf(x)dx and ∫abf(x)dx=−∫baf(x)dx.
1. Given values:
-
∫12−10f(x)dx=6⟹∫−1012f(x)dx=−6
-
∫100−10f(x)dx=−2⟹∫−10100f(x)dx=2
-
∫100−5f(x)dx=4⟹∫−5100f(x)dx=−4
2. Find ∫−512f(x)dx:
We can break the integral from −5 to 12 using the intermediate points −10 and 100:
3. Substitute the known values:
Correct Option:
(b) -12
Explanation
Solving:
We use the property ∫abf(x)dx=∫acf(x)dx+∫cbf(x)dx and ∫abf(x)dx=−∫baf(x)dx.
1. Given values:
-
∫12−10f(x)dx=6⟹∫−1012f(x)dx=−6
-
∫100−10f(x)dx=−2⟹∫−10100f(x)dx=2
-
∫100−5f(x)dx=4⟹∫−5100f(x)dx=−4
2. Find ∫−512f(x)dx:
We can break the integral from −5 to 12 using the intermediate points −10 and 100:
3. Substitute the known values:
Correct Option:
(b) -12