Obraich a-mach an fharsaingeachd eadar an lùb \(y = {x^3}\) agus an \(x\)-axis.
\[- \frac{1}{4}\,aonada{n^2}\]
\[\frac{1}{4}\,aonada{n^2}\]
\[\frac{1}{2}\,aonada{n^2}\]
Tha an diagram a' sealltainn na farsaingeachd a tha taobh a-staigh nan lùban eadar \(y = {x^3} - 3{x^2} + 4\) agus \(y = {x^2} - x - 2\) eadar \(x = - 1\) agus \(x = 2\).
Seall an fharsaingeachd dhathte mar iontagral.
\[\int\limits_{ - 1}^2 {{x^3}} - 4{x^2} + x + 6\,dx\]
\[\int\limits_{ - 1}^2 { - {x^3}} + 4{x^2} - x - 6\,dx\]
\[\int\limits_{ - 1}^2 {{x^3}} - 4{x^2} - x + 2\,dx\]
Obraich a-mach an fharsaingeachd a tha eadar an dà lùb ann an ceist 2.
\[\frac{{167}}{{12}}\,aonada{n^2}\]
\[\frac{{45}}{4}\,aonada{n^2}\]
\[\frac{{41}}{{12}}\,aonada{n^2}\]
Obraich a-mach na co-chomharran aig P agus Q.
\[P(1,0)\,agus\,Q(2,0)\]
\[P( - 2,0)\,agus\,Q( - 1,0)\]
\[P(2,0)\,agus\,Q(4,0)\]
Obraich a-mach an fharsaingeachd a tha eadar an dà lùb \(x\)-axis ann an ceist 4.
\[\frac{{23}}{{12}}\,aonada{n^2}\]
\[\frac{7}{{12}}\,aonada{n^2}\]
\[\frac{5}{2}\,aonada{n^2}\]
Tha lùb sa bheil \(\frac{{dy}}{{dx}} = 3{x^2} + 1\) a' dol tron phuing \(( - 1,2)\).
Sgrìobh \(y\) ann an teirmean de \(x\).
\[y = {x^3} + x + 4\]
\[y = {x^3} + x - 1\]
\[y = {x^3} + x + 2\]
Lorg abairt airson \(f(x)\) gus am bi \(f\textquotesingle(x)= 4{x^3} - 1\) agus \(f(2) = - 1\).
\[f(x) = {x^4} - x - 1\]
\[f(x) = {x^4} - x - 15\]
\[f(x) = {x^4} - x\]