Integral x√16 - x² dx

Integral x√16 – x² dx

Jawab:

$displaystyletext{misal:}\u=16-x^2\du=-2x,dx\\int xsqrt{16-x^2},dx=intsqrt{16-x^2}cdotfrac{-2}{-2}x,dx\int xsqrt{16-x^2},dx=-frac{1}{2}intsqrt{16-x^2}cdot(-2x),dx\int xsqrt{16-x^2},dx=-frac{1}{2}int u^frac12,du\int xsqrt{16-x^2},dx=-frac{1}{2}cdotfrac1{displaystylefrac12+1}u^{frac12+1}+C\int xsqrt{16-x^2},dx=-frac{1}{2}cdotfrac2{3}u^{frac32}+C\int xsqrt{16-x^2},dx=-frac1{3}(16-x^2)^{frac32}+C$

Beberapa konsep yang dipakai:

$displaystyletriangleright~int ky,dx=kint y,dx\triangleright~int ax^n,dx=frac{a}{n+1}x^{n+1}+C~;~nneq-1$