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અનિયત સંકલન

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ગણિત ધોરણ 12 સિમેસ્ટર 4

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ગણિત

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અનિયત સંકલન

નીચેનાં વિધેયનું x વિશે સંકલિત મેળવો :
$straight x squared space log space straight x space semicolon space straight x space greater than space 0$

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નીચેનાં વિધેયનું x વિશે સંકલિત મેળવો :
$cos to the power of negative 1 end exponent space straight x space semicolon space straight x space element of space open square brackets negative 1 comma space 1 close square brackets$

straight I space equals space integral space cos to the power of negative 1 end exponent space straight x space dx

equals space integral space 1 space times space cos to the power of negative 1 end exponent space straight x space dx equals space cos to the power of negative 1 end exponent space straight x space integral space 1 space dx space minus space integral space open square brackets straight d over dx space cos to the power of negative 1 end exponent space straight x space integral space 1 space dx close square brackets space dx equals space straight x space cos to the power of negative 1 end exponent space straight x space minus space integral space minus space fraction numerator 1 over denominator square root of 1 space minus space straight x squared end root end fraction space times space straight x space dx space equals space straight x space cos to the power of negative 1 end exponent space straight x space plus space straight I subscript 1 જ ્ ય ાં comma space straight I subscript 1 space equals space integral space fraction numerator straight x over denominator square root of 1 space minus space straight x squared end root end fraction space dx space semicolon space square root of 1 space minus space straight x squared end root space equals space straight t space space લ ે ત ાં comma 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 fraction numerator 1 over denominator 2 square root of 1 space minus space straight x squared end root end fraction space open parentheses negative 2 straight x close parentheses space dx space equals space dt therefore space straight I subscript 1 space equals space integral space minus space dt space equals space minus straight t space plus space straight c space equals space minus space square root of 1 space minus space straight x squared end root space plus space straight c therefore space straight I space equals space straight x space cos to the power of negative 1 end exponent space straight x space minus space square root of 1 space minus space straight x squared end root space plus space straight c therefore space integral space cos to the power of negative 1 end exponent space straight x space dx space equals bold space bold x bold space bold cos to the power of bold minus bold 1 end exponent bold space bold x bold space bold minus bold space square root of bold 1 bold space bold minus bold space bold x to the power of bold 2 end root bold space bold plus bold space bold c

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નીચેનાં વિધેયનું x વિશે સંકલિત મેળવો :
$straight x squared space straight e to the power of 3 straight x end exponent$

નીચેનાં વિધેયનું x વિશે સંકલિત મેળવો :
(3 + 5x) cos 7x

નીચેનાં વિધેયનું x વિશે સંકલિત મેળવો :
$straight x squared space tan to the power of negative 1 end exponent space straight x$

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