10:[["$","title","0",{"children":"CUET Mathematics - The value of _-/2^/2(x^5 + x^3 x)dx is | PYQs + Solutions | AfterBoards"}],["$","meta","1",{"name":"description","content":"undefined Given: _-/2^/2(x^5 + x^3 x)dx For any odd function f(x) where f(-x) = -f(x): _-a^af(x)dx = 0 The negative side cancels the positive side.

Breaking the integral into two parts: _-/2^/2(x^5 + x^3 x)dx = _-/2^/2x^5 dx + _-/2^/2x^3 x dx

Consider f(x) = x^5 f(-x) = (-x)^5 f(-x) = -x^5 f(-x) = -f(x) Therefore x^5 is an odd function. _-/2^/2x^5 dx = 0

Consider g(x) = x^3 x g(-x) = (-x)^3 (-x) g(-x) = -x^3 x Since (-x) = x: g(-x) = -g(x) Therefore x^3 x is an odd function. _-/2^/2x^3 x dx = 0

_-/2^/2(x^5 + x^3 x)dx = 0 + 0 _-/2^/2(x^5 + x^3 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"}],["$","meta","7",{"property":"og:title","content":"CUET Mathematics - The value of _-/2^/2(x^5 + x^3 x)dx is | PYQs + Solutions"}],["$","meta","8",{"property":"og:description","content":"undefined Given: _-/2^/2(x^5 + x^3 x)dx For any odd function f(x) where f(-x) = -f(x): _-a^af(x)dx = 0 The negative side cancels the positive side.

Breaking the integral into two parts: _-/2^/2(x^5 + x^3 x)dx = _-/2^/2x^5 dx + _-/2^/2x^3 x dx

Consider f(x) = x^5 f(-x) = (-x)^5 f(-x) = -x^5 f(-x) = -f(x) Therefore x^5 is an odd function. _-/2^/2x^5 dx = 0

Consider g(x) = x^3 x g(-x) = (-x)^3 (-x) g(-x) = -x^3 x Since (-x) = x: g(-x) = -g(x) Therefore x^3 x is an odd function. _-/2^/2x^3 x dx = 0

_-/2^/2(x^5 + x^3 x)dx = 0 + 0 _-/2^/2(x^5 + x^3 x)dx = 0"}],["$","meta","9",{"property":"og:url","content":"https://www.afterboards.in/past-year-questions/cuet-mathematics/2025/slot-18/29"}],["$","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"}],["$","meta","15",{"name":"twitter:title","content":"CUET Mathematics - The value of _-/2^/2(x^5 + x^3 x)dx is | PYQs + Solutions"}],["$","meta","16",{"name":"twitter:description","content":"undefined Given: _-/2^/2(x^5 + x^3 x)dx For any odd function f(x) where f(-x) = -f(x): _-a^af(x)dx = 0 The negative side cancels the positive side.

Breaking the integral into two parts: _-/2^/2(x^5 + x^3 x)dx = _-/2^/2x^5 dx + _-/2^/2x^3 x dx

Consider f(x) = x^5 f(-x) = (-x)^5 f(-x) = -x^5 f(-x) = -f(x) Therefore x^5 is an odd function. _-/2^/2x^5 dx = 0

Consider g(x) = x^3 x g(-x) = (-x)^3 (-x) g(-x) = -x^3 x Since (-x) = x: g(-x) = -g(x) Therefore x^3 x is an odd function. _-/2^/2x^3 x dx = 0

_-/2^/2(x^5 + x^3 x)dx = 0 + 0 _-/2^/2(x^5 + x^3 x)dx = 0"}],["$","meta","17",{"name":"twitter:image","content":"https://www.afterboards.in/pyp/AfterBoards%20CUET%20Past%20Year%20Papers%20with%20Solutions.webp"}],["$","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 2 June Shift 1 PYQs

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