Tolong kaka dan abang yang baik hati
4
∫
2 (-x2 + 6x - 8) dx
4
∫
2 (-x2 + 6x - 8) dx
Takamori37
Integralkan secara biasa.
2 votes
Thanks 2
Kilos
![\int\limits^4_2 {-x^{2} + 6x - 8} \, dx \\\\ = [-\frac{1}{3}x^{2} + \frac{6}{2}x^{2} - 8x]^4_2 \\\\ = [-\frac{1}{3}x^{3} + 3x^{2}- 8x]^4_2 \\\\ = (-\frac{1}{3}(4)^{3} + 3(4)^{2} - 8(4))- (-\frac{1}{3}(2)^{3} + 3(2)^{2} - 8(2)) \\\\ = (-\frac{64}{3} + 48 - 32) - (-\frac{8}{3} + 12- 16) \\\\ = - \frac{64}{3} + \frac{8}{3} + 16 + 4 \\\\ = - \frac{56}{3} + 20 \\\\ = \frac{-56}{3} + \frac{60}{3} \\\\ \boxed { \boxed { \bold { = \frac{4}{3} } } }](https://tex.z-dn.net/?f=+%5Cint%5Climits%5E4_2+%7B-x%5E%7B2%7D+%2B+6x+-+8%7D+%5C%2C+dx+%5C%5C%5C%5C+%3D++%5B-%5Cfrac%7B1%7D%7B3%7Dx%5E%7B2%7D+%2B+%5Cfrac%7B6%7D%7B2%7Dx%5E%7B2%7D+-+8x%5D%5E4_2+%5C%5C%5C%5C+%3D+%5B-%5Cfrac%7B1%7D%7B3%7Dx%5E%7B3%7D+%2B+3x%5E%7B2%7D-+8x%5D%5E4_2+%5C%5C%5C%5C+%3D+%28-%5Cfrac%7B1%7D%7B3%7D%284%29%5E%7B3%7D+%2B+3%284%29%5E%7B2%7D+-+8%284%29%29-+%28-%5Cfrac%7B1%7D%7B3%7D%282%29%5E%7B3%7D+%2B+3%282%29%5E%7B2%7D+-+8%282%29%29+%5C%5C%5C%5C+%3D+%28-%5Cfrac%7B64%7D%7B3%7D+%2B+48+-+32%29+-+%28-%5Cfrac%7B8%7D%7B3%7D+%2B+12-+16%29+%5C%5C%5C%5C+%3D+-+%5Cfrac%7B64%7D%7B3%7D+%2B+%5Cfrac%7B8%7D%7B3%7D+%2B+16+%2B+4+%5C%5C%5C%5C+%3D+-+%5Cfrac%7B56%7D%7B3%7D+%2B+20+%5C%5C%5C%5C+%3D+%5Cfrac%7B-56%7D%7B3%7D+%2B+%5Cfrac%7B60%7D%7B3%7D+%5C%5C%5C%5C+%5Cboxed+%7B+%5Cboxed+%7B+%5Cbold+%7B+%3D+%5Cfrac%7B4%7D%7B3%7D+%7D+%7D+%7D "\int\limits^4_2 {-x^{2} + 6x - 8} \, dx \\\\ = [-\frac{1}{3}x^{2} + \frac{6}{2}x^{2} - 8x]^4_2 \\\\ = [-\frac{1}{3}x^{3} + 3x^{2}- 8x]^4_2 \\\\ = (-\frac{1}{3}(4)^{3} + 3(4)^{2} - 8(4))- (-\frac{1}{3}(2)^{3} + 3(2)^{2} - 8(2)) \\\\ = (-\frac{64}{3} + 48 - 32) - (-\frac{8}{3} + 12- 16) \\\\ = - \frac{64}{3} + \frac{8}{3} + 16 + 4 \\\\ = - \frac{56}{3} + 20 \\\\ = \frac{-56}{3} + \frac{60}{3} \\\\ \boxed { \boxed { \bold { = \frac{4}{3} } } }")
2 votes
Thanks 2