Question

Evaluate $integral subscript 0 superscript straight pi space 5 space left parenthesis 5 minus 4 space cosθ right parenthesis to the power of 1 fourth end exponent space sin space straight theta space dθ$

Solution

Let I = $integral subscript 0 superscript straight pi 5 space left parenthesis 5 minus 4 cosθ right parenthesis to the power of 1 fourth end exponent space sin space straight theta space dθ space equals space 5 integral subscript 0 superscript straight pi left parenthesis 5 minus 4 space cosθ right parenthesis to the power of 1 fourth end exponent space sin space straight theta space dθ$
Put $5 minus 4 space cosθ space equals space straight y comma space space therefore space space 4 space sin space straight theta space dθ space equals space dy space rightwards double arrow space space space sin space straight theta space dθ space equals space 1 fourth dy$
When $straight theta space equals 0 comma space space straight y space equals space 5 minus 4 space cos space 0 space equals space 5 minus 4 space equals space 1$
When $straight theta space equals space straight pi comma space space straight y space equals space 5 minus 4 space cosπ space equals space 5 minus 4 left parenthesis negative 1 right parenthesis space equals space 5 plus 4 space equals space 9$
$therefore$ I = $5 over 4 integral subscript 1 superscript 9 straight y to the power of 1 fourth end exponent dy space equals space 5 over 4 open square brackets fraction numerator straight y to the power of begin display style 5 over 4 end style end exponent over denominator begin display style 5 over 4 end style end fraction close square brackets subscript 1 superscript 9 space equals space open square brackets straight y to the power of 5 over 4 end exponent close square brackets subscript 1 superscript 9$ $equals left parenthesis 9 right parenthesis to the power of 5 over 4 end exponent minus 1 space equals space left parenthesis 3 squared right parenthesis to the power of 5 over 4 end exponent minus 1 space equals space 3 to the power of 5 over 2 end exponent minus 1 space equals space left parenthesis 3 to the power of 5 right parenthesis to the power of 1 half end exponent minus 1 space equals space left parenthesis 81 cross times 3 right parenthesis to the power of 1 half end exponent minus 1 space equals space 9 square root of 3 minus 1$

For Daily Free Study Material Join wiredfaculty

Integrals

Evaluate $integral subscript 0 superscript straight pi space 5 space left parenthesis 5 minus 4 space cosθ right parenthesis to the power of 1 fourth end exponent space sin space straight theta space dθ$

Some More Questions From Integrals Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Loaction