Question

given that \\(\int_{1}^{6} f(x) dx = \frac{35}{13}\\), what is \\(\int_{6}^{1} f(w) dw\\)?
\\(\int_{6}^{1} f(w) dw = \\)

Explanation:

Step1: Recall reverse interval rule

$\int_{a}^{b} f(x)dx = -\int_{b}^{a} f(x)dx$

Step2: Apply rule to given integral

$\int_{6}^{1} f(w)dw = -\int_{1}^{6} f(w)dw$

Step3: Substitute known integral value

$\int_{6}^{1} f(w)dw = -\frac{35}{13}$

Answer:

$\boldsymbol{-\frac{35}{13}}$