10:[["$","title","0",{"children":"CUET Mathematics - _-^ e^ xe^ x + e^- xdx is equal to | PYQs + Solutions | AfterBoards"}],["$","meta","1",{"name":"description","content":"undefined Given integral: _-^ e^ xe^ x + e^- xdx

Let I = _-^ e^ xe^ x + e^- xdx ... (1)

Using the property _-a^a f(x)dx = _-a^a f(-x)dx, replace x with -x: I = _-^ e^(-x)e^(-x) + e^-(-x)dx Since (-x) = -(x): I = _-^ e^- xe^- x + e^ xdx ... (2)

Adding equations (1) and (2): I + I = _-^ e^ xe^ x + e^- xdx + _-^ e^- xe^- x + e^ xdx 2I = _-^ [e^ x + e^- xe^ x + e^- x]dx 2I = _-^ 1 dx

2I = [x]_-^ 2I = - (-) 2I = 2 I = Therefore, the integral equals ."}],["$","link","2",{"rel":"manifest","href":"https://www.afterboards.in/manifest.json","crossOrigin":"$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"}],["$","meta","7",{"property":"og:title","content":"CUET Mathematics - _-^ e^ xe^ x + e^- xdx is equal to | PYQs + Solutions"}],["$","meta","8",{"property":"og:description","content":"undefined Given integral: _-^ e^ xe^ x + e^- xdx

Let I = _-^ e^ xe^ x + e^- xdx ... (1)

Using the property _-a^a f(x)dx = _-a^a f(-x)dx, replace x with -x: I = _-^ e^(-x)e^(-x) + e^-(-x)dx Since (-x) = -(x): I = _-^ e^- xe^- x + e^ xdx ... (2)

Adding equations (1) and (2): I + I = _-^ e^ xe^ x + e^- xdx + _-^ e^- xe^- x + e^ xdx 2I = _-^ [e^ x + e^- xe^ x + e^- x]dx 2I = _-^ 1 dx

2I = [x]_-^ 2I = - (-) 2I = 2 I = Therefore, the integral equals ."}],["$","meta","9",{"property":"og:url","content":"https://www.afterboards.in/past-year-questions/cuet-mathematics/2025/slot-4/36"}],["$","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"}],["$","meta","15",{"name":"twitter:title","content":"CUET Mathematics - _-^ e^ xe^ x + e^- xdx is equal to | PYQs + Solutions"}],["$","meta","16",{"name":"twitter:description","content":"undefined Given integral: _-^ e^ xe^ x + e^- xdx

Let I = _-^ e^ xe^ x + e^- xdx ... (1)

Using the property _-a^a f(x)dx = _-a^a f(-x)dx, replace x with -x: I = _-^ e^(-x)e^(-x) + e^-(-x)dx Since (-x) = -(x): I = _-^ e^- xe^- x + e^ xdx ... (2)

Adding equations (1) and (2): I + I = _-^ e^ xe^ x + e^- xdx + _-^ e^- xe^- x + e^ xdx 2I = _-^ [e^ x + e^- xe^ x + e^- x]dx 2I = _-^ 1 dx

2I = [x]_-^ 2I = - (-) 2I = 2 I = Therefore, the integral equals ."}],["$","meta","17",{"name":"twitter:image","content":"https://www.afterboards.in/pyp/AfterBoards%20CUET%20Past%20Year%20Papers%20with%20Solutions.webp"}],["$","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"}],["$","link","21",{"rel":"icon","href":"https://www.afterboards.in/icons/android/android-launchericon-512-512.png","sizes":"512x512","type":"image/png"}],["$","link","22",{"rel":"icon","href":"https://www.afterboards.in/icons/android/android-launchericon-192-192.png","sizes":"192x192","type":"image/png"}],"$L17","$L18","$L19","$L1a"]

CUET Mathematics 2025 14 May Shift 2 PYQs

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