9:{"metadata":[["$","title","0",{"children":"2024 Slot 1 - _0^/2 1- xcosec x+ x d x= | PYQs + Solutions | AfterBoards"}],["$","meta","1",{"name":"description","content":"undefined _0^/2 1- xcosec x+ x dx Let's simplify the integrand by converting everything in terms of x and x. Remember that x = x x and cosec x = 1 x.

Substituting these into our integrand: 1- xcosec x+ x = 1- x x1 x+ x Simplifying the numerator: 1- x x = x - x x Now our integrand becomes: x - x x1 x+ x = x - x x x1+ x x = x - x1+ x x

Let's use the substitution u = 2 - x, then: - du = -dx - When x = 0, u = 2 - When x = 2, u = 0 Under this substitution: - u = x - u = x

Applying the substitution to the integral: _0^/2 x - x1+ x x dx = _/2^0 u - u1+ u u (-du) = _0^/2 u - u1+ u u du

Let's call our original integral I: I = _0^/2 x - x1+ x x dx From our substitution, we also know: I = _0^/2 u - u1+ u u du Renaming u back to x in the second integral: I = _0^/2 x - x1+ x x dx Adding these equal values: 2I = _0^/2 x - x1+ x x dx + _0^/2 x - x1+ x x dx 2I = _0^/2 ( x - x) + ( x - x)1+ x x dx = _0^/2 01+ x x dx = 0

Therefore, I = 0 _0^/2 1- xcosec x+ x dx = 0"}],["$","link","2",{"rel":"manifest","href":"https://www.afterboards.in/manifest.json","crossOrigin":"$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"}],["$","meta","7",{"property":"og:title","content":"2024 Slot 1 - _0^/2 1- xcosec x+ x d x= | PYQs + Solutions"}],["$","meta","8",{"property":"og:description","content":"undefined _0^/2 1- xcosec x+ x dx Let's simplify the integrand by converting everything in terms of x and x. Remember that x = x x and cosec x = 1 x.

Substituting these into our integrand: 1- xcosec x+ x = 1- x x1 x+ x Simplifying the numerator: 1- x x = x - x x Now our integrand becomes: x - x x1 x+ x = x - x x x1+ x x = x - x1+ x x

Let's use the substitution u = 2 - x, then: - du = -dx - When x = 0, u = 2 - When x = 2, u = 0 Under this substitution: - u = x - u = x

Applying the substitution to the integral: _0^/2 x - x1+ x x dx = _/2^0 u - u1+ u u (-du) = _0^/2 u - u1+ u u du

Therefore, I = 0 _0^/2 1- xcosec x+ x dx = 0"}],["$","meta","9",{"property":"og:url","content":"https://www.afterboards.in/cuet-past-year-questions/cuet-mat-2024-01/24"}],["$","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"}],["$","meta","15",{"name":"twitter:title","content":"2024 Slot 1 - _0^/2 1- xcosec x+ x d x= | PYQs + Solutions"}],["$","meta","16",{"name":"twitter:description","content":"undefined _0^/2 1- xcosec x+ x dx Let's simplify the integrand by converting everything in terms of x and x. Remember that x = x x and cosec x = 1 x.

Substituting these into our integrand: 1- xcosec x+ x = 1- x x1 x+ x Simplifying the numerator: 1- x x = x - x x Now our integrand becomes: x - x x1 x+ x = x - x x x1+ x x = x - x1+ x x

Let's use the substitution u = 2 - x, then: - du = -dx - When x = 0, u = 2 - When x = 2, u = 0 Under this substitution: - u = x - u = x

Applying the substitution to the integral: _0^/2 x - x1+ x x dx = _/2^0 u - u1+ u u (-du) = _0^/2 u - u1+ u u du

Therefore, I = 0 _0^/2 1- xcosec x+ x dx = 0"}],"$L18","$L19","$L1a","$L1b","$L1c","$L1d","$L1e","$L1f","$L20","$L21"],"error":null,"digest":"$undefined"}

2024 Slot 1 PYQs

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