IIT JEE , AIEEE Forum - Mathematics , Differential Calculus

rishipratimm

_^find1

^a [x] f `(x)dx, =

a)af([a])-{f(1)+f(2)+??f(a)}

b)af(a)-{f(1)+f(2)+??f([a])}

c)[a]f(a)-{f(1)+f(2)+??f([a])}

d)[a]f([a])-{f(1)+f(2)+??f(a)}

when a>1

rathin_123

plz write proparly

LAMPARD

Split the integral as
₁

² f'(x)dx +2₂

³ f'(x)dx + 3 ₃

⁴ f'(x)dx and so on till (a-1)_a-1

^a f'(x)dx.
=> f(2)-f(1) + 2[f(3)-f(2)] + 3[f(4)-f(3)] +4[f(5)-f(4)] and so on till (a-1)[f(a)-f(a-1)]
=> -[f(1)+f(2)+f(3)+....+f(a-1)] + (a-1)f(a)
Can you make the options more clearer???

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