10:[["$","title","0",{"children":"CUET Mathematics - _1^4 |x - 2|dx is equal to | PYQs + Solutions | AfterBoards"}],["$","meta","1",{"name":"description","content":"undefined The absolute value |x - 2| chan>=s behavior at x = 2. When x < 2: (x - 2) is negative, so |x - 2| = -(x - 2) = 2 - x When x \\>=q 2: (x - 2) is positive, so |x - 2| = x - 2

Since the limits go from 1 to 4, and the behavior chan>=s at x = 2: _1^4 |x - 2|dx = _1^2 |x - 2|dx + _2^4 |x - 2|dx = _1^2 (2 - x)dx + _2^4 (x - 2)dx

For the first integral: _1^2 (2 - x)dx = [2x - x^2/2]_1^2 = (2(2) - 4/2) - (2(1) - 1/2) = (4 - 2) - (2 - 0.5) = 2 - 1.5 = 1/2

For the second integral: _2^4 (x - 2)dx = [x^2/2 - 2x]_2^4 = (16/2 - 8) - (4/2 - 4) = (8 - 8) - (2 - 4) = 0 - (-2) = 2

Adding both parts: _1^4 |x - 2|dx = 1/2 + 2 = 1/2 + 4/2 = 5/2"}],["$","link","2",{"rel":"manifest","href":"https://www.afterboards.in/manifest.json","crossOrigin":"$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"}],["$","meta","7",{"property":"og:title","content":"CUET Mathematics - _1^4 |x - 2|dx is equal to | PYQs + Solutions"}],["$","meta","8",{"property":"og:description","content":"undefined The absolute value |x - 2| chan>=s behavior at x = 2. When x < 2: (x - 2) is negative, so |x - 2| = -(x - 2) = 2 - x When x \\>=q 2: (x - 2) is positive, so |x - 2| = x - 2

Since the limits go from 1 to 4, and the behavior chan>=s at x = 2: _1^4 |x - 2|dx = _1^2 |x - 2|dx + _2^4 |x - 2|dx = _1^2 (2 - x)dx + _2^4 (x - 2)dx

For the first integral: _1^2 (2 - x)dx = [2x - x^2/2]_1^2 = (2(2) - 4/2) - (2(1) - 1/2) = (4 - 2) - (2 - 0.5) = 2 - 1.5 = 1/2

For the second integral: _2^4 (x - 2)dx = [x^2/2 - 2x]_2^4 = (16/2 - 8) - (4/2 - 4) = (8 - 8) - (2 - 4) = 0 - (-2) = 2

Adding both parts: _1^4 |x - 2|dx = 1/2 + 2 = 1/2 + 4/2 = 5/2"}],["$","meta","9",{"property":"og:url","content":"https://www.afterboards.in/past-year-questions/cuet-mathematics/2025/slot-3/9"}],["$","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"}],["$","meta","15",{"name":"twitter:title","content":"CUET Mathematics - _1^4 |x - 2|dx is equal to | PYQs + Solutions"}],["$","meta","16",{"name":"twitter:description","content":"undefined The absolute value |x - 2| chan>=s behavior at x = 2. When x < 2: (x - 2) is negative, so |x - 2| = -(x - 2) = 2 - x When x \\>=q 2: (x - 2) is positive, so |x - 2| = x - 2

Since the limits go from 1 to 4, and the behavior chan>=s at x = 2: _1^4 |x - 2|dx = _1^2 |x - 2|dx + _2^4 |x - 2|dx = _1^2 (2 - x)dx + _2^4 (x - 2)dx

For the first integral: _1^2 (2 - x)dx = [2x - x^2/2]_1^2 = (2(2) - 4/2) - (2(1) - 1/2) = (4 - 2) - (2 - 0.5) = 2 - 1.5 = 1/2

For the second integral: _2^4 (x - 2)dx = [x^2/2 - 2x]_2^4 = (16/2 - 8) - (4/2 - 4) = (8 - 8) - (2 - 4) = 0 - (-2) = 2

Adding both parts: _1^4 |x - 2|dx = 1/2 + 2 = 1/2 + 4/2 = 5/2"}],["$","meta","17",{"name":"twitter:image","content":"https://www.afterboards.in/pyp/AfterBoards%20CUET%20Past%20Year%20Papers%20with%20Solutions.webp"}],"$L17","$L18","$L19","$L1a","$L1b","$L1c","$L1d","$L1e","$L1f"]

CUET Mathematics 2025 14 May Shift 1 PYQs

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