10:[["$","title","0",{"children":"CUET Mathematics - _0^8 (x^2/3 + 1) dx is equal to | PYQs + Solutions | AfterBoards"}],["$","meta","1",{"name":"description","content":"undefined The integral can be split into two parts: _0^8 (x^2/3 + 1) dx = _0^8 x^2/3 dx + _0^8 1 dx

Using the power ru<= with n = 2/3: n + 1 = 2/3 + 1 = 5/3 x^2/3 dx = x^5/35/3 = 3/5x^5/3 For the constant: 1 dx = x

Combining the results: _0^8 (x^2/3 + 1) dx = [3/5x^5/3 + x]_0^8

Evaluating 8^5/3: 8^5/3 = (8^1/3)^5 8^1/3 = 2 (2)^5 = 32 At x = 8: 3/5(32) + 8 = 96/5 + 40/5 = 136/5

At x = 0: 3/5(0)^5/3 + 0 = 0

The final result: 136/5 - 0 = 136/5 Therefore, _0^8 (x^2/3 + 1) dx = 1365"}],["$","link","2",{"rel":"manifest","href":"https://www.afterboards.in/manifest.json","crossOrigin":"$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"}],["$","meta","7",{"property":"og:title","content":"CUET Mathematics - _0^8 (x^2/3 + 1) dx is equal to | PYQs + Solutions"}],["$","meta","8",{"property":"og:description","content":"undefined The integral can be split into two parts: _0^8 (x^2/3 + 1) dx = _0^8 x^2/3 dx + _0^8 1 dx

Using the power ru<= with n = 2/3: n + 1 = 2/3 + 1 = 5/3 x^2/3 dx = x^5/35/3 = 3/5x^5/3 For the constant: 1 dx = x

Combining the results: _0^8 (x^2/3 + 1) dx = [3/5x^5/3 + x]_0^8

Evaluating 8^5/3: 8^5/3 = (8^1/3)^5 8^1/3 = 2 (2)^5 = 32 At x = 8: 3/5(32) + 8 = 96/5 + 40/5 = 136/5

At x = 0: 3/5(0)^5/3 + 0 = 0

The final result: 136/5 - 0 = 136/5 Therefore, _0^8 (x^2/3 + 1) dx = 1365"}],["$","meta","9",{"property":"og:url","content":"https://www.afterboards.in/past-year-questions/cuet-mathematics/2025/slot-20/15"}],["$","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"}],["$","meta","15",{"name":"twitter:title","content":"CUET Mathematics - _0^8 (x^2/3 + 1) dx is equal to | PYQs + Solutions"}],["$","meta","16",{"name":"twitter:description","content":"undefined The integral can be split into two parts: _0^8 (x^2/3 + 1) dx = _0^8 x^2/3 dx + _0^8 1 dx

Using the power ru<= with n = 2/3: n + 1 = 2/3 + 1 = 5/3 x^2/3 dx = x^5/35/3 = 3/5x^5/3 For the constant: 1 dx = x

Combining the results: _0^8 (x^2/3 + 1) dx = [3/5x^5/3 + x]_0^8

Evaluating 8^5/3: 8^5/3 = (8^1/3)^5 8^1/3 = 2 (2)^5 = 32 At x = 8: 3/5(32) + 8 = 96/5 + 40/5 = 136/5

At x = 0: 3/5(0)^5/3 + 0 = 0

The final result: 136/5 - 0 = 136/5 Therefore, _0^8 (x^2/3 + 1) dx = 1365"}],["$","meta","17",{"name":"twitter:image","content":"https://www.afterboards.in/pyp/AfterBoards%20CUET%20Past%20Year%20Papers%20with%20Solutions.webp"}],["$","link","18",{"rel":"shortcut icon","href":"https://www.afterboards.in/favicon.ico","type":"image/x-icon","sizes":"48x48"}],["$","link","19",{"rel":"icon","href":"https://www.afterboards.in/favicon.ico","type":"image/x-icon","sizes":"48x48"}],["$","link","20",{"rel":"icon","href":"https://www.afterboards.in/icons/windows11/Square44x44Logo.altform-lightunplated_targetsize-256.png","sizes":"256x256","type":"image/png"}],["$","link","21",{"rel":"icon","href":"https://www.afterboards.in/icons/android/android-launchericon-512-512.png","sizes":"512x512","type":"image/png"}],"$L17","$L18","$L19","$L1a","$L1b"]

CUET Mathematics 2025 3 June Shift 2 PYQs

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