Question

Give a formula for $f(x)$ given that $f$ is continuous and $-2x^6 + x^4 - 1 = \int_0^x \frac{f(t)}{t+1} dt$. $\circ f(x) = -\frac{2}{7}x^7 + \frac{1}{5}x^5 - x$ $\circ f(x) = -\frac{2}{7}x^8 - \frac{2}{7}x^7 + \frac{1}{5}x^6 + \frac{1}{5}x^5 - x^2 - x$ $\circ f(x) = -2x^6 + x^4 - 1$ $\circ f(x) = -12x^6 - 12x^5 + 4x^4 + 4x^3$ $\circ f(x) = -12x^5 + 4x^3$ $\circ$ None of the above.

          Give a formula for $f(x)$ given that $f$ is continuous and $-2x^6 + x^4 - 1 = \int_0^x \frac{f(t)}{t+1} dt$.

$\circ f(x) = -\frac{2}{7}x^7 + \frac{1}{5}x^5 - x$

$\circ f(x) = -\frac{2}{7}x^8 - \frac{2}{7}x^7 + \frac{1}{5}x^6 + \frac{1}{5}x^5 - x^2 - x$

$\circ f(x) = -2x^6 + x^4 - 1$

$\circ f(x) = -12x^6 - 12x^5 + 4x^4 + 4x^3$

$\circ f(x) = -12x^5 + 4x^3$

$\circ$ None of the above.

Give a formula for f(x) given that f is continuous and -2x^6 + x^4 - 1 = ∫0^x (f(t))/(t+1) dt.

∘ f(x) = -(2)/(7)x^7 + (1)/(5)x^5 - x

∘ f(x) = -(2)/(7)x^8 - (2)/(7)x^7 + (1)/(5)x^6 + (1)/(5)x^5 - x^2 - x

∘ f(x) = -2x^6 + x^4 - 1

∘ f(x) = -12x^6 - 12x^5 + 4x^4 + 4x^3

∘ f(x) = -12x^5 + 4x^3

∘ None of the above.

Added by Julian M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

01/10/2023

Step 1

Step 1: We are given the equation -2x^(6) + x^(4) - 1 = ∫_0^x (f(t))/(t+1)dt. Show more…

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Give a formula for f(x) given that f is continuous and -2x^(6)+x^(4)-1=int_0^x (f(t))/(t+1)dt. f(x)=-(2)/(7)x^(7)+(1)/(5)x^(5)-x f(x)=-(2)/(7)x^(8)-(2)/(7)x^(7)+(1)/(5)x^(6)+(1)/(5)x^(5)-x^(2)-x f(x)=-2x^(6)+x^(4)-1 f(x)=-12x^(6)-12x^(5)+4x^(4)+4x^(3) f(x)=-12x^(5)+4x^(3) None of the above. f (t) dt t+1 Give a formula for f(x) given that f is continuous and --2 x + x4 --1 : 2 1 T 5 Ofx= - Ofx O f() = 2x6 + x4 - 1 O f(x) = -12x6 - 12x5 + 4x4 + 4x3 O f(x)= -12x5 + 4x3 O None of the above.