Find the whole area of the circle x² + y² = a².

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Solution

The equation of circle is x² + y² = a² ...(1)
Its centre is origin and radius a. We know that circle x² + y² = a² is symmetrical about both axes.

therefore space space space required space area space equals space 4 space integral subscript 0 superscript straight a straight y space dx space equals space 4 space integral subscript 0 superscript straight a square root of straight a squared minus straight x squared end root space dx

equals space 4 open square brackets fraction numerator straight x square root of straight a squared minus straight x squared end root over denominator 2 end fraction plus straight a squared over 2 sin to the power of negative 1 end exponent straight x over straight a close square brackets subscript 0 superscript straight a equals space 4 open square brackets open parentheses 0 plus straight a squared over 2 sin to the power of negative 1 end exponent 1 close parentheses space minus space open parentheses 0 plus straight a squared over 2 sin to the power of negative 1 end exponent 0 close parentheses close square brackets equals space 4 open square brackets open parentheses 0 plus straight a squared over 2 sin to the power of negative 1 end exponent 1 close parentheses space minus space open parentheses 0 plus straight a squared over 2 sin to the power of negative 1 end exponent 0 close parentheses close square brackets equals 4 space open square brackets straight a squared over 2 cross times straight pi over 2 close square brackets space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space open square brackets because space sin to the power of negative 1 end exponent 0 space equals space 0 close square brackets space equals space straight pi space straight a space.

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Vector Algebra

Find the whole area of the circle x² + y² = a².

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Vector Algebra

Find the whole area of the circle x2 + y2 = a2.

Some More Questions From Vector Algebra Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Find the whole area of the circle x² + y² = a².