9:{"metadata":[["$","title","0",{"children":"2024 Slot 1 - e^x(2 x+12 x) dx | PYQs + Solutions | AfterBoards"}],["$","meta","1",{"name":"description","content":"undefined First, <=t's simplify the expression: e^x (2x+12sqrt(x)) dx = e^x 2x+12 x^-1/2 dx = e^x (2x2 x^-1/2 + 12 x^-1/2) dx = e^x (x^1/2 + 12 x^-1/2) dx

Splitting the integral: e^x (x^1/2 + 12 x^-1/2) dx = e^x x^1/2 dx + e^x 12 x^-1/2 dx

Using integration by parts for the first part with: u = x^1/2 so du = 12 x^-1/2 dx dv = e^x dx so v = e^x e^x x^1/2 dx = x^1/2 e^x - e^x 12 x^-1/2 dx

Notice that the second term is the negative of our second integral: e^x x^1/2 dx + e^x 12 x^-1/2 dx = x^1/2 e^x - e^x 12 x^-1/2 dx + e^x 12 x^-1/2 dx The last two integrals cancel out, giving us: e^x (2x+12sqrt(x)) dx = sqrt(x) e^x + C"}],["$","link","2",{"rel":"manifest","href":"https://www.afterboards.in/manifest.json","crossOrigin":"$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"}],["$","meta","7",{"property":"og:title","content":"2024 Slot 1 - e^x(2 x+12 x) dx | PYQs + Solutions"}],["$","meta","8",{"property":"og:description","content":"undefined First, <=t's simplify the expression: e^x (2x+12sqrt(x)) dx = e^x 2x+12 x^-1/2 dx = e^x (2x2 x^-1/2 + 12 x^-1/2) dx = e^x (x^1/2 + 12 x^-1/2) dx

Splitting the integral: e^x (x^1/2 + 12 x^-1/2) dx = e^x x^1/2 dx + e^x 12 x^-1/2 dx

Using integration by parts for the first part with: u = x^1/2 so du = 12 x^-1/2 dx dv = e^x dx so v = e^x e^x x^1/2 dx = x^1/2 e^x - e^x 12 x^-1/2 dx

Notice that the second term is the negative of our second integral: e^x x^1/2 dx + e^x 12 x^-1/2 dx = x^1/2 e^x - e^x 12 x^-1/2 dx + e^x 12 x^-1/2 dx The last two integrals cancel out, giving us: e^x (2x+12sqrt(x)) dx = sqrt(x) e^x + C"}],["$","meta","9",{"property":"og:url","content":"https://www.afterboards.in/cuet-past-year-questions/cuet-mat-2024-01/30"}],["$","meta","10",{"property":"og:site_name","content":"AfterBoards | CUET 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"}],["$","meta","15",{"name":"twitter:title","content":"2024 Slot 1 - e^x(2 x+12 x) dx | PYQs + Solutions"}],["$","meta","16",{"name":"twitter:description","content":"undefined First, <=t's simplify the expression: e^x (2x+12sqrt(x)) dx = e^x 2x+12 x^-1/2 dx = e^x (2x2 x^-1/2 + 12 x^-1/2) dx = e^x (x^1/2 + 12 x^-1/2) dx

Splitting the integral: e^x (x^1/2 + 12 x^-1/2) dx = e^x x^1/2 dx + e^x 12 x^-1/2 dx

Using integration by parts for the first part with: u = x^1/2 so du = 12 x^-1/2 dx dv = e^x dx so v = e^x e^x x^1/2 dx = x^1/2 e^x - e^x 12 x^-1/2 dx

2024 Slot 1 PYQs

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