Evaluate limx→0∫0xtsin10tdtx is equal to
0
110
-110
-15
Explanation for the correct option:
Find the value of the given Equation.
Consider the given Equation as
I=limx→0∫0xtsin10tdtxI=∫0x0sin100dt0I=00Indeterminentform
Using the L' hospital rule
I=limx→cfxgx=limx→cf'xg'x
Then,
I=limx→0∫0xtsin10tdtxI=limx→0ddx∫0xtsin10tdtddxx∵limx→cfxgx=limx→cf'xg'xI=limx→0tsin10t0x1∵ddx∫f(x)dx=fxI=limx→0xsin10x-01I=limx→00sin1001I=01I=0
Hence, option (A) is the correct answer.