10:[["$","title","0",{"children":"CUET Mathematics - _/6^/3 dx1 + sqrt(tanx) is equal to | PYQs + Solutions | AfterBoards"}],["$","meta","1",{"name":"description","content":"undefined Let I = _/6^/3 dx1 + sqrt( x) ... (1)

Using King's Property: _a^b f(x)dx = _a^b f(a+b-x)dx Here a + b = /6 + /3 = /2 Replace x with /2 - x: I = _/6^/3 dx1 + sqrt((/2 - x)) ... (2)

Using the identity (/2 - x) = x = 1/ x: I = _/6^/3 dx1 + sqrt(1/ x) I = _/6^/3 dx1 + 1sqrt( x) Multiply numerator and denominator by sqrt( x): I = _/6^/3 sqrt( x)sqrt( x) + 1 dx ... (3)

Adding equations (1) and (3): 2I = _/6^/3 (11 + sqrt( x) + sqrt( x)1 + sqrt( x)) dx 2I = _/6^/3 1 + sqrt( x)1 + sqrt( x) dx 2I = _/6^/3 1 dx

2I = [x]_/6^/3 2I = /3 - /6 2I = 2/6 - /6 = /6 I = /12

/12"}],["$","link","2",{"rel":"manifest","href":"https://www.afterboards.in/manifest.json","crossOrigin":"$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"}],["$","meta","7",{"property":"og:title","content":"CUET Mathematics - _/6^/3 dx1 + sqrt(tanx) is equal to | PYQs + Solutions"}],["$","meta","8",{"property":"og:description","content":"undefined Let I = _/6^/3 dx1 + sqrt( x) ... (1)

Using King's Property: _a^b f(x)dx = _a^b f(a+b-x)dx Here a + b = /6 + /3 = /2 Replace x with /2 - x: I = _/6^/3 dx1 + sqrt((/2 - x)) ... (2)

Using the identity (/2 - x) = x = 1/ x: I = _/6^/3 dx1 + sqrt(1/ x) I = _/6^/3 dx1 + 1sqrt( x) Multiply numerator and denominator by sqrt( x): I = _/6^/3 sqrt( x)sqrt( x) + 1 dx ... (3)

Adding equations (1) and (3): 2I = _/6^/3 (11 + sqrt( x) + sqrt( x)1 + sqrt( x)) dx 2I = _/6^/3 1 + sqrt( x)1 + sqrt( x) dx 2I = _/6^/3 1 dx

2I = [x]_/6^/3 2I = /3 - /6 2I = 2/6 - /6 = /6 I = /12

/12"}],["$","meta","9",{"property":"og:url","content":"https://www.afterboards.in/past-year-questions/cuet-mathematics/2025/slot-1/30"}],["$","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"}],["$","meta","15",{"name":"twitter:title","content":"CUET Mathematics - _/6^/3 dx1 + sqrt(tanx) is equal to | PYQs + Solutions"}],["$","meta","16",{"name":"twitter:description","content":"undefined Let I = _/6^/3 dx1 + sqrt( x) ... (1)

Using King's Property: _a^b f(x)dx = _a^b f(a+b-x)dx Here a + b = /6 + /3 = /2 Replace x with /2 - x: I = _/6^/3 dx1 + sqrt((/2 - x)) ... (2)

Using the identity (/2 - x) = x = 1/ x: I = _/6^/3 dx1 + sqrt(1/ x) I = _/6^/3 dx1 + 1sqrt( x) Multiply numerator and denominator by sqrt( x): I = _/6^/3 sqrt( x)sqrt( x) + 1 dx ... (3)

Adding equations (1) and (3): 2I = _/6^/3 (11 + sqrt( x) + sqrt( x)1 + sqrt( x)) dx 2I = _/6^/3 1 + sqrt( x)1 + sqrt( x) dx 2I = _/6^/3 1 dx

2I = [x]_/6^/3 2I = /3 - /6 2I = 2/6 - /6 = /6 I = /12

/12"}],["$","meta","17",{"name":"twitter:image","content":"https://www.afterboards.in/pyp/AfterBoards%20CUET%20Past%20Year%20Papers%20with%20Solutions.webp"}],["$","link","18",{"rel":"shortcut icon","href":"https://www.afterboards.in/favicon.ico","type":"image/x-icon","sizes":"48x48"}],["$","link","19",{"rel":"icon","href":"https://www.afterboards.in/favicon.ico","type":"image/x-icon","sizes":"48x48"}],"$L17","$L18","$L19","$L1a","$L1b","$L1c","$L1d"]

CUET Mathematics 2025 13 May Shift 1 PYQs

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