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Integrals

Question
CBSEENMA12032393

Explain the following integral:
space integral subscript 0 superscript 1 fraction numerator 1 over denominator 1 plus straight x squared end fraction dx

Solution

Let I = integral subscript 0 superscript 1 fraction numerator dx over denominator 1 plus straight x squared end fraction space equals space left square bracket tan to the power of negative 1 end exponent straight x right square bracket subscript 0 superscript 1 space equals space tan to the power of negative 1 end exponent 1 minus tan to the power of negative 1 end exponent 0 space equals space straight pi over 4 minus 0 space equals space straight pi over 4

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