Questions
If the equality
holds for all x such that then a and b are given by
detailed solution
Correct option is A
∫0x btcos4t−asin4tt2dt=b∫0xcos4ttdt-a∫0xsin4tt2 dt=b∫0x cos4ttdt−a−sin4tt0x+4∫0x cos4ttdt=(b−4a)∫0x cos4ttdt+asin4xx−4aThus (b−4a)∫0xxcos4ttdt+ asin4xx−4a=asin4xx−1i.e. (b−4a)∫0xxcos4ttdt=4a-1.Since R.H.S. is independent of x, so we must have b−4a=0 and 4a−1=0 i.e., a=1/4,b=1.Similar Questions
The value of is
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