Let . Without evaluating any integrals, determine the value of in terms of and…

MATHEMATICS · Subjective · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

Let

A=\displaystyle \int_{1}^{5}\bigl(u(x)-v(x)\bigr)\,dx

. Without evaluating any integrals, determine the value of

\displaystyle \int_{1}^{5}\bigl(u(x)+7-(v(x)+7)\bigr)\,dx

in terms of

A

and briefly explain why your answer holds.