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Integrals — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsIntegrals1 Mark
MCQ
$\int_0^4\left(e^{2 x}+x\right) d x$ is equal to
  • A
    $\frac{15+e^8}{2}$
  • B
    $\frac{16-e^8}{2}$
  • ✓
    $\frac{e^8-15}{2}$
  • D
    $\frac{-e^8-15}{2}$
✓

Answer

Correct option: C.
$\frac{e^8-15}{2}$
$\text {Let } I=\int_0^4\left(e^{2 x}+x\right)$
$d x=\left[\frac{e^{2 x}}{2}+\frac{x^2}{2}\right]_0^4$
$=\frac{e^8}{2}+\frac{16}{2}-\frac{e^0}{2}-0$
$=\frac{e^8}{2}+\frac{16}{2}-\frac{1}{2}$
$=\frac{e^8+15}{2}$

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