explain what is wrong with the following use of the power rule.\n∫5/x² dx = 5/(x³/3)+c\n\nchoose the correct…
explain what is wrong with the following use of the power rule.\n∫5/x² dx = 5/(x³/3)+c\n\nchoose the correct answer below.\na. the power rule was applied to the numerator rather than the entire integrand.\nb. the arbitrary constant is not required when the power rule is used.\nc. the power rule for derivatives was used instead of the power rule for integrals.\nd. the power rule was applied to the denominator rather than the entire integrand.
Answer
Brief Explanations:
The power - rule for integrals is $\int x^n dx=\frac{x^{n + 1}}{n+1}+C$ ($n\neq - 1$). In the given integral $\int\frac{5}{x^2}dx = 5\int x^{-2}dx$. The correct application of the power - rule for integrals gives $5\times\frac{x^{-2 + 1}}{-2+1}+C=- \frac{5}{x}+C$. The error in the given work is that the power - rule for derivatives $\frac{d}{dx}(x^n)=nx^{n - 1}$ was used instead of the power - rule for integrals.
Answer:
C. The power rule for derivatives was used instead of the power rule for integrals.