Identify $u$ and $d u / d x$ for the integral $\int \sqrt { 1 - x ^ { 11 } } \left( - 11 x ^ { 10 } \right) d x$ .
A) $u = 1 - x ^ { 11 }$ and $d u / d x = - 12 x$
B) $u = 1 - x ^ { 11 }$ and $d u / d x = - 11 x ^ { 10 }$
C) $u = \sqrt { 1 - x ^ { 11 } }$ and $d u / d x = - 11 x ^ { 10 }$
D) $u= 1 - x ^ { 11 }$ and $d u / d x = 11 x$
E) $u = \sqrt { 1 - x ^ { 11 } }$ and $d u / d x = 12 x$

Question

Quizplus · Accepted Answer

For the integral $\int \sqrt { 1 - x ^ { 11 } } \left( - 11 x ^ { 10 } \right) d x$, setting $u = 1 - x ^ { 11 }$ simplifies the inside of the square root. Differentiating $u$ with respect to $x$ gives $du/dx = -11x^{10}$, matching the multiplier of the square root in the integral.

Identify uuu And du/dxd u / d xdu/dx For the Integral ∫1−x11(−11x10)dx\int \sqrt { 1 - x ^ { 11 } } \left( - 11 x ^ { 10 } \right) d x∫1−x11​(−11x10)dx

Identify $u$ And $d u / d x$ For the Integral $\int \sqrt { 1 - x ^ { 11 } } \left( - 11 x ^ { 10 } \right) d x$