10:[["$","title","0",{"children":"CUET Mathematics - _sqrt(_e 2)^sqrt(_e 4) xe^x^2 dx is equal to | PYQs + Solutions | AfterBoards"}],["$","meta","1",{"name":"description","content":"undefined The lower limit is sqrt(_e 2) = sqrt( 2) The upper limit is sqrt(_e 4) = sqrt( 4) = sqrt((2^2)) = sqrt(2 2)

Let u = x^2 Then du/dx = 2x du = 2x dx x dx = 1/2 du

xe^x^2 dx = e^u 1/2 du = 1/2 e^u du = 1/2 e^u + C = 1/2 e^x^2 + C

_sqrt( 2)^sqrt(2 2) xe^x^2 dx = [1/2 e^x^2]_sqrt( 2)^sqrt(2 2) = 1/2 e^(sqrt(2 2))^2 - 1/2 e^(sqrt( 2))^2 = 1/2 e^2 2 - 1/2 e^ 2

Since e^ a = a: e^ 2 = 2 e^2 2 = e^ 2^2 = 2^2 = 4

= 1/2(4) - 1/2(2) = 2 - 1 = 1 Therefore, the value of the integral is 1."}],["$","link","2",{"rel":"manifest","href":"https://www.afterboards.in/manifest.json","crossOrigin":"$undefined"}],["$","meta","3",{"name":"keywords","content":"CUETMAT,MAT,Calculus,Integrals"}],["$","meta","4",{"name":"robots","content":"index, follow"}],["$","meta","5",{"name":"category","content":"education"}],["$","meta","6",{"name":"google-site-verification","content":"google"}],["$","meta","7",{"property":"og:title","content":"CUET Mathematics - _sqrt(_e 2)^sqrt(_e 4) xe^x^2 dx is equal to | PYQs + Solutions"}],["$","meta","8",{"property":"og:description","content":"undefined The lower limit is sqrt(_e 2) = sqrt( 2) The upper limit is sqrt(_e 4) = sqrt( 4) = sqrt((2^2)) = sqrt(2 2)

Let u = x^2 Then du/dx = 2x du = 2x dx x dx = 1/2 du

xe^x^2 dx = e^u 1/2 du = 1/2 e^u du = 1/2 e^u + C = 1/2 e^x^2 + C

_sqrt( 2)^sqrt(2 2) xe^x^2 dx = [1/2 e^x^2]_sqrt( 2)^sqrt(2 2) = 1/2 e^(sqrt(2 2))^2 - 1/2 e^(sqrt( 2))^2 = 1/2 e^2 2 - 1/2 e^ 2

Since e^ a = a: e^ 2 = 2 e^2 2 = e^ 2^2 = 2^2 = 4

= 1/2(4) - 1/2(2) = 2 - 1 = 1 Therefore, the value of the integral is 1."}],["$","meta","9",{"property":"og:url","content":"https://www.afterboards.in/past-year-questions/cuet-mathematics/2025/slot-17/14"}],["$","meta","10",{"property":"og:site_name","content":"AfterBoards | CUET Mathematics Preparation"}],["$","meta","11",{"property":"og:image","content":"https://www.afterboards.in/pyp/AfterBoards%20CUET%20Past%20Year%20Papers%20with%20Solutions.webp"}],["$","meta","12",{"property":"og:type","content":"website"}],["$","meta","13",{"name":"twitter:card","content":"summary_large_image"}],["$","meta","14",{"name":"twitter:site","content":"afterboards.in"}],["$","meta","15",{"name":"twitter:title","content":"CUET Mathematics - _sqrt(_e 2)^sqrt(_e 4) xe^x^2 dx is equal to | PYQs + Solutions"}],["$","meta","16",{"name":"twitter:description","content":"undefined The lower limit is sqrt(_e 2) = sqrt( 2) The upper limit is sqrt(_e 4) = sqrt( 4) = sqrt((2^2)) = sqrt(2 2)

Let u = x^2 Then du/dx = 2x du = 2x dx x dx = 1/2 du

xe^x^2 dx = e^u 1/2 du = 1/2 e^u du = 1/2 e^u + C = 1/2 e^x^2 + C

_sqrt( 2)^sqrt(2 2) xe^x^2 dx = [1/2 e^x^2]_sqrt( 2)^sqrt(2 2) = 1/2 e^(sqrt(2 2))^2 - 1/2 e^(sqrt( 2))^2 = 1/2 e^2 2 - 1/2 e^ 2

Since e^ a = a: e^ 2 = 2 e^2 2 = e^ 2^2 = 2^2 = 4

= 1/2(4) - 1/2(2) = 2 - 1 = 1 Therefore, the value of the integral is 1."}],["$","meta","17",{"name":"twitter:image","content":"https://www.afterboards.in/pyp/AfterBoards%20CUET%20Past%20Year%20Papers%20with%20Solutions.webp"}],["$","link","18",{"rel":"shortcut icon","href":"https://www.afterboards.in/favicon.ico","type":"image/x-icon","sizes":"48x48"}],["$","link","19",{"rel":"icon","href":"https://www.afterboards.in/favicon.ico","type":"image/x-icon","sizes":"48x48"}],["$","link","20",{"rel":"icon","href":"https://www.afterboards.in/icons/windows11/Square44x44Logo.altform-lightunplated_targetsize-256.png","sizes":"256x256","type":"image/png"}],["$","link","21",{"rel":"icon","href":"https://www.afterboards.in/icons/android/android-launchericon-512-512.png","sizes":"512x512","type":"image/png"}],"$L17","$L18","$L19","$L1a","$L1b"]

CUET Mathematics 2025 30 May Shift 2 PYQs

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