Advertisements
Advertisements
प्रश्न
If `d/dx f(x) = 2x + 3/x` and f(1) = 1, then f(x) is ______.
पर्याय
x2 + 3 log | x | + 1
x2 + 3 log | x |
`2 - 3/x^2`
x2 + 3 log | x | – 4
Advertisements
उत्तर
If `d/dx f(x) = 2x + 3/x` and f(1) = 1, then f(x) is x2 + 3 log | x |.
Explanation:
Given,
`d/dx [f(x)] = 2x + 3/x`
On integrating both sides,
`int d/dx [f(x)]dx = int(2x + 3/x)dx`
`\implies` f(x) = `(2x^2)/2 + 3 log |x| + C`
= x2 + 3 log | x | + C
Given: f(1) = 1
∴ f(1) = (1)2 + 3 × log 1 + C
`\implies` 1 = 1 + 0 + C
`\implies` C = 0
∴ f(x) = x2 + 3 log | x |.
APPEARS IN
संबंधित प्रश्न
Find `int dx/(5 - 8x - x^2)`
Find `int (cos theta)/((4 + sin^2 theta)(5 - 4 cos^2 theta)) d theta`
Evaluate `int (cos 2x + 2sin^2x)/(cos^2x) dx`
Evaluate : \[\int\limits_0^\frac{\pi}{4} \tan x dx\] .
Evaluate: `int ("sin 2x")/((1 + "sin x")(2 + "sin x")) "dx"`
Prove that `int_0^"a" "f(x)" "dx" = int_0^"a" "f"("a"-"x")"dx"` ,and hence evaluate `int_0^1 "x"^2(1 - "x")^"n""dx"`.
Evaluate the following:
`int x/(sqrt(x) + 1) "d"x` (Hint: Put `sqrt(x)` = z)
Evaluate the following:
`int sqrt(("a" + x)/("a" - x)) "d"x`
Evaluate the following:
`int x^(1/2)/(1 + x^(3/4)) "d"x` (Hint: Put `sqrt(x)` = z4)
The value of the integral `int_(-1)^2 [x] dx` is
`int (sin^8x - cos^8x)/(1 - 2sin^2x cos^2x) dx` is equal to
`int_0^oo (dx)/((x^2 + a^2)(x^2 + b^2))` is
Evaluate: `int_0^(pi/2) cosx/(( cos x/2 + sin x/2)^3) dx`
Which expression gives the indefinite integral of \[f'(x)\]?
Differentiation and indefinite integration are what type of processes?
If \[\frac{d}{dx}[F(x)]=\frac{d}{dx}[G(x)],\] what follows?
Which formula is the Difference Rule?
For a constant \[k,\] which expression is the Constant Multiple Rule?
What is integration by the method of inspection?
Find an antiderivative of \[\cos 2x.\]
Evaluate \[\int\operatorname{cosec}x(\operatorname{cosec}x+\cot x)\,dx.\]
Find the antiderivative \[F\] of \[f(x)=4x^3-6\] satisfying \[F(0)=3.\]
