A' fuasgladh cho-aontaran diofarachail
Nuair a bhios sinn ag iontaigeadh abairtean sìmplidh, 's dòcha nach bi fios againn air a' chunbhal iontaigidh, an teirm \(+ c\). Thèid againn air luach \(c\) obrachadh a-mach nuair a gheibh sinn fiosrachadh a bharrachd bhon cheist.
Eisimpleir (leudachadh)
Obraich a-mach co-aontar na lùib far a bheil \(\frac{{dy}}{{dx}} = 4{x^3} + 6{x^2}\) agus e a' dol tron phuing \((1,3)\).
Fuasgladh
\(y = \int {(4{x^3}} + 6{x^2})\,\,dx = {x^4} + 2{x^3} + c\)
Ag ionadachadh \(x = 1\) agus \(y = 3\) (bhon cho-chomharra sa cheist):
\(y = {x^4} + 2{x^3} + c\)
\(3 = {1^4} + 2{(1)^3} + c\)
\(3 = 3 + c\)
\(c = 0\)
Mar sin 's e co-chomharra na lùib \(y = {x^4} + 2{x^3}\)
Question
Leudachadh
Obraich a-mach co-aontar na lùib far a bheil \(\frac{{dy}}{{dx}} = 2x + 1\) agus e a' dol tron phuing \((2,9)\).
\(y = \int {(2x + 1)} \,\,dx = {x^2} + x + c\)
Ag ionadachadh \(x = 2\) agus \(y = 9\):
\(9 = 4 + 2 + c\)
\(c = 3\)
\(y = {x^2} + x + 3\)
Mar sin 's e co-chomharra na lùib \(y = {x^2} + x + 3\)
Question
Leudachadh
Tha an caiseadAir graf, 's e an caisead claonadh na loidhne. Mar as motha an caisead, 's ann as motha a tha reat an atharrachaidh. aig tansaint don lùb aig \(f\textquotesingle(x)= 6x - \frac{5}{{{x^2}}}\). Obraich a-mach co-aontar na lùib ma tha e a' dol tron phuing \((1,6)\).
\(f(x) = \int {6x-\frac{5}{{{x^2}}}}\,\,dx\)
\(= \int {(6x}-5{x^{ - 2}})\,\,dx\)
\(f(x) = \frac{{6{x^2}}}{2} - \frac{{5{x^{ - 1}}}}{{ - 1}} + c\)
\(f(x) = 3{x^2} + \frac{5}{x} + c\)
Ionadaich nuair a tha \(x = 1\) agus \(y = 6\):
\(6 = 3{(1)^2} + \frac{5}{1} + c\)
\(6 = 8 + c\)
\(c = - 2\)
Mar sin 's e co-aontar na lùib \(f(x) = 3{x^2} + \frac{5}{x} - 2\)
