10:[["$","title","0",{"children":"CUET Mathematics - The value of _0^1 x e^x dx is: | PYQs + Solutions | AfterBoards"}],["$","meta","1",{"name":"description","content":"undefined When integrating a product of different types of functions like x and e^x, use integration by parts. u dv = uv - v du Using the ILATE ru<= (Inverse, Logarithmic, Al>=braic, Trigonometric, Exponential), choose the function that appears first as u. Let u = x (Al>=braic) and dv = e^x dx (Exponential) Then du = dx and v = e^x

Applying integration by parts: x e^x dx = x e^x - e^x dx = x e^x - e^x + C = e^x(x - 1) + C

Evaluating the definite integral from 0 to 1: _0^1 x e^x dx = [e^x(x - 1)]_0^1 At x = 1: e^1(1 - 1) = 0 At x = 0: e^0(0 - 1) = -1

_0^1 x e^x dx = 0 - (-1) = 1 Therefore, the value 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"}],["$","meta","7",{"property":"og:title","content":"CUET Mathematics - The value of _0^1 x e^x dx is: | PYQs + Solutions"}],["$","meta","8",{"property":"og:description","content":"undefined When integrating a product of different types of functions like x and e^x, use integration by parts. u dv = uv - v du Using the ILATE ru<= (Inverse, Logarithmic, Al>=braic, Trigonometric, Exponential), choose the function that appears first as u. Let u = x (Al>=braic) and dv = e^x dx (Exponential) Then du = dx and v = e^x

Applying integration by parts: x e^x dx = x e^x - e^x dx = x e^x - e^x + C = e^x(x - 1) + C

Evaluating the definite integral from 0 to 1: _0^1 x e^x dx = [e^x(x - 1)]_0^1 At x = 1: e^1(1 - 1) = 0 At x = 0: e^0(0 - 1) = -1

_0^1 x e^x dx = 0 - (-1) = 1 Therefore, the value is 1."}],["$","meta","9",{"property":"og:url","content":"https://www.afterboards.in/past-year-questions/cuet-mathematics/2025/slot-8/3"}],["$","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"}],["$","meta","15",{"name":"twitter:title","content":"CUET Mathematics - The value of _0^1 x e^x dx is: | PYQs + Solutions"}],["$","meta","16",{"name":"twitter:description","content":"undefined When integrating a product of different types of functions like x and e^x, use integration by parts. u dv = uv - v du Using the ILATE ru<= (Inverse, Logarithmic, Al>=braic, Trigonometric, Exponential), choose the function that appears first as u. Let u = x (Al>=braic) and dv = e^x dx (Exponential) Then du = dx and v = e^x

Applying integration by parts: x e^x dx = x e^x - e^x dx = x e^x - e^x + C = e^x(x - 1) + C

Evaluating the definite integral from 0 to 1: _0^1 x e^x dx = [e^x(x - 1)]_0^1 At x = 1: e^1(1 - 1) = 0 At x = 0: e^0(0 - 1) = -1

_0^1 x e^x dx = 0 - (-1) = 1 Therefore, the value 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"}],"$L17","$L18","$L19","$L1a","$L1b","$L1c","$L1d","$L1e"]

CUET Mathematics 2025 19 May Shift 1 PYQs

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