What is #f(x) = int -x^3+x-4 dx# if #f(2) = -3 #?

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Answer 1 · 2017-07-25T02:31:52

#f(x) = int(-x^3+x-4)dx#

Use the power rule to integrate.

# = -x^4/4+x^2/2-4x+C# #" "# (item 1)

Find #C# by using the fact that #f(2) = -3#

#f(x) = -(2)^4/4+(2)^2/2-4(2) + C = -3#

#-4+2-8+C=-3#

# - 10 +C = -3#

# C = 7# #" "# (item 2)

Combining items (1) and (2), we finish with

#f(x) = -x^4/4+x^2/2-4x+7#