10:[["$","title","0",{"children":"CUET Mathematics - _0^/2 sqrt(1 - 2x) dx is equal to: | PYQs + Solutions | AfterBoards"}],["$","meta","1",{"name":"description","content":"undefined sqrt(1 - 2x) can be simplified using 2x = 2 x x: 1 - 2x = 1 - 2 x x

Expanding ( x - x)^2: ( x - x)^2 = ^2 x - 2 x x + ^2 x = 1 - 2 x x Therefore: sqrt(1 - 2x) = sqrt(( x - x)^2) = | x - x|

For x [0, /2], the sign of x - x chan>=s at x = /4: - At x = 0: 0 = 0 < 0 = 1 - At x = /4: (/4) = (/4) - At x = /2: (/2) = 1 > (/2) = 0 So: | x - x| = cases x - x & for 0 \\<=q x \\<=q /4 \\\\ x - x & for /4 \\<=q x \\<=q /2 cases

The integral splits at x = /4: _0^/2 sqrt(1 - 2x) dx = _0^/4 ( x - x) dx + _/4^/2 ( x - x) dx

For the first integral: _0^/4 ( x - x) dx = [ x + x]_0^/4 = (sqrt(2)2 + sqrt(2)2) - (0 + 1) = sqrt(2) - 1

For the second integral: _/4^/2 ( x - x) dx = [- x - x]_/4^/2 = (0 - 1) - (-sqrt(2)2 - sqrt(2)2) = -1 + sqrt(2) = sqrt(2) - 1

The total value: (sqrt(2) - 1) + (sqrt(2) - 1) = 2(sqrt(2) - 1) Therefore, the answer is 2(sqrt(2) - 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"}],["$","meta","7",{"property":"og:title","content":"CUET Mathematics - _0^/2 sqrt(1 - 2x) dx is equal to: | PYQs + Solutions"}],["$","meta","8",{"property":"og:description","content":"undefined sqrt(1 - 2x) can be simplified using 2x = 2 x x: 1 - 2x = 1 - 2 x x

Expanding ( x - x)^2: ( x - x)^2 = ^2 x - 2 x x + ^2 x = 1 - 2 x x Therefore: sqrt(1 - 2x) = sqrt(( x - x)^2) = | x - x|

The integral splits at x = /4: _0^/2 sqrt(1 - 2x) dx = _0^/4 ( x - x) dx + _/4^/2 ( x - x) dx

For the first integral: _0^/4 ( x - x) dx = [ x + x]_0^/4 = (sqrt(2)2 + sqrt(2)2) - (0 + 1) = sqrt(2) - 1

For the second integral: _/4^/2 ( x - x) dx = [- x - x]_/4^/2 = (0 - 1) - (-sqrt(2)2 - sqrt(2)2) = -1 + sqrt(2) = sqrt(2) - 1

The total value: (sqrt(2) - 1) + (sqrt(2) - 1) = 2(sqrt(2) - 1) Therefore, the answer is 2(sqrt(2) - 1)."}],["$","meta","9",{"property":"og:url","content":"https://www.afterboards.in/past-year-questions/cuet-mathematics/2025/slot-10/33"}],["$","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"}],["$","meta","15",{"name":"twitter:title","content":"CUET Mathematics - _0^/2 sqrt(1 - 2x) dx is equal to: | PYQs + Solutions"}],["$","meta","16",{"name":"twitter:description","content":"undefined sqrt(1 - 2x) can be simplified using 2x = 2 x x: 1 - 2x = 1 - 2 x x

Expanding ( x - x)^2: ( x - x)^2 = ^2 x - 2 x x + ^2 x = 1 - 2 x x Therefore: sqrt(1 - 2x) = sqrt(( x - x)^2) = | x - x|

The integral splits at x = /4: _0^/2 sqrt(1 - 2x) dx = _0^/4 ( x - x) dx + _/4^/2 ( x - x) dx

For the first integral: _0^/4 ( x - x) dx = [ x + x]_0^/4 = (sqrt(2)2 + sqrt(2)2) - (0 + 1) = sqrt(2) - 1

For the second integral: _/4^/2 ( x - x) dx = [- x - x]_/4^/2 = (0 - 1) - (-sqrt(2)2 - sqrt(2)2) = -1 + sqrt(2) = sqrt(2) - 1

The total value: (sqrt(2) - 1) + (sqrt(2) - 1) = 2(sqrt(2) - 1) Therefore, the answer is 2(sqrt(2) - 1)."}],"$L17","$L18","$L19","$L1a","$L1b","$L1c","$L1d","$L1e","$L1f","$L20"]

CUET Mathematics 2025 21 May Shift 2 PYQs

Keyboard Shortcuts