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Let f: Rvec(0,1) be a continuous functio...

Let `f: Rvec(0,1)` be a continuous function. Then, which of the following function (s) has (have) the value zero at some point in the interval (0,1)? `e^x-int_0^xf(t)sintdt` (b) `f(x)+int_0^(pi/2)f(t)sintdt` `x-int_0^(pi/2-x)f(t)costdt` (d) `x^9-f(x)`

A

`e^( x) - int_(0)^(x) f(t) sin t dt`

B

`f(x ) = int_(0)^(pi/2) f(t) sin t dt`

C

`x-int_(0)^(pi/2 to x) f( t) cot dt`

D

`x^(9) -f( x)`

Text Solution

Verified by Experts

The correct Answer is:
C, D
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