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7.1 inderfinite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.1 inderfinite integral1 Mark
MCQ
If $f'(x) = {x^2} + 5$ and $f(0) = - 1$, then $f(x) = $
  • A
    ${x^3} + 5x - 1$
  • B
    ${x^3} + 5x + 1$
  • ✓
    $\frac{1}{3}{x^3} + 5x - 1$
  • D
    $\frac{1}{3}{x^3} + 5x + 1$
✓

Answer

Correct option: C.
$\frac{1}{3}{x^3} + 5x - 1$
c
(c) Given that $f'(x) = {x^2} + 5$ and $f(0) = - 1$
==> $f(x) = \frac{{{x^3}}}{3} + 5x + c$. If $x = 0,$ then $f(0) = c$

==> $c = - 1$.
Hence $f(x) = \frac{{{x^3}}}{3} + 5x - 1.$

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