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 \([0, 2 \pi]\).

Difficulty level: Easy task (using definitions and simple reasoning)
Routine calculation training
Cs translation
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