Area calculations
Task number: 3143
Calculate the area
Variant 1
determined by the parabola \(y = x^2\) on the interval \([0, t]\).
Variant 2
of circle with radius \(r\).
Variant 3
of ellipse with a semi-major axis length of \(a\) a semi-minor axis length of \(b\).
Variant 4
under the sine curve on \([0,\pi]\).
Variant 5
under the function \(\sin^2 x\) on \([0,\pi]\). (Try to find the least demanding procedure)
Variant 6
in between the curves \(y = \frac1x\), \(y = \frac1{x^2}\) and \(x=2\).
Variant 7
between the functions \(\sin x\) and \(\cos x\) on \([0, 2 \pi]\).
