Failed to connect to MySQL: Access denied for user 'examnext_online'@'localhost' (using password: YES) If ƒ(x) = `a + bx + cx^2`, whre c > 0 and `b^2` – 4ac < 0, then the area enclosed by the coordinate axes, the line x = 2 and the curve y = ƒ(x) is given by - Sarthaks eConnect

If ƒ(x) = `a + bx + cx^2`, whre c > 0 and `b^2` – 4ac < 0, then the area enclosed by the coordinate axes, the line x = 2 and the curve y = ƒ(x) is given by :

If ƒ(x) = `a + bx + cx^2`, whre c > 0 and `b^2` – 4ac < 0, then the area enclosed by the coordinate axes, the line x = 2 and the curve y = ƒ(x) is given by :

A.

`1/3{4f(1) + f(2)}`

B.

`1/2 { f(0)+4f(1)+f(2)}`

C.

`1/2 {f(0)+4f(1)}`

D.

`1/3 { f(0)+4 f (1)+ f (2)}`

Solution

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Best answer

Area =`int_0^2(a+bxc+cx^2)dx`

`= 2a+2b+8/3c`

= `1/3 [6a 6b 8c]` ..........(i)

But, ƒ(x) = a + bx + `cx^3`

ƒ(0) = a,

ƒ(1) = a + b + c

`ƒ(2) = a + 2b + 4c`

`1/3{ƒ(0)+4ƒ(1)+ƒ(2)}`

`1/3 {a+4(a+b+c)+(a+2b+4)}`

`1/3(6a+6b+8c)`