10:[["$","title","0",{"children":"CUET Mathematics - The value of _-a^a f(x)dx where f(x) = 7^x/1+7^x is: | PYQs + Solutions | AfterBoards"}],["$","meta","1",{"name":"description","content":"undefined We need to find _-a^a f(x)dx where f(x) = 7^x/1+7^x. The limits are symmetric around zero, sug>=sting special symmetry properties.

Substitute -x into the function: f(-x) = 7^-x1+7^-x Multiply both numerator and denominator by 7^x: f(-x) = 7^-x1+7^-x 7^x/7^x f(-x) = 7^-x 7^x(1+7^-x) 7^x f(-x) = 1/7^x + 1 f(-x) = 1/1+7^x

Add f(x) and f(-x): f(x) + f(-x) = 7^x/1+7^x + 1/1+7^x f(x) + f(-x) = 7^x + 1/1+7^x f(x) + f(-x) = 1+7^x/1+7^x f(x) + f(-x) = 1

Let I = _-a^a f(x)dx Replace x with -x using substitution. With symmetric limits, the integral remains unchan>=d: I = _-a^a f(-x)dx

Add the two forms: I + I = _-a^a f(x)dx + _-a^a f(-x)dx 2I = _-a^a [f(x) + f(-x)]dx 2I = _-a^a 1 dx 2I = x|_-a^a 2I = a - (-a) 2I = 2a I = a Therefore, _-a^a f(x)dx = a"}],["$","link","2",{"rel":"manifest","href":"https://www.afterboards.in/manifest.json","crossOrigin":"$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"}],["$","meta","7",{"property":"og:title","content":"CUET Mathematics - The value of _-a^a f(x)dx where f(x) = 7^x/1+7^x is: | PYQs + Solutions"}],["$","meta","8",{"property":"og:description","content":"undefined We need to find _-a^a f(x)dx where f(x) = 7^x/1+7^x. The limits are symmetric around zero, sug>=sting special symmetry properties.

Substitute -x into the function: f(-x) = 7^-x1+7^-x Multiply both numerator and denominator by 7^x: f(-x) = 7^-x1+7^-x 7^x/7^x f(-x) = 7^-x 7^x(1+7^-x) 7^x f(-x) = 1/7^x + 1 f(-x) = 1/1+7^x

Add f(x) and f(-x): f(x) + f(-x) = 7^x/1+7^x + 1/1+7^x f(x) + f(-x) = 7^x + 1/1+7^x f(x) + f(-x) = 1+7^x/1+7^x f(x) + f(-x) = 1

Let I = _-a^a f(x)dx Replace x with -x using substitution. With symmetric limits, the integral remains unchan>=d: I = _-a^a f(-x)dx

Add the two forms: I + I = _-a^a f(x)dx + _-a^a f(-x)dx 2I = _-a^a [f(x) + f(-x)]dx 2I = _-a^a 1 dx 2I = x|_-a^a 2I = a - (-a) 2I = 2a I = a Therefore, _-a^a f(x)dx = a"}],["$","meta","9",{"property":"og:url","content":"https://www.afterboards.in/past-year-questions/cuet-mathematics/2025/slot-18/55"}],["$","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"}],["$","meta","15",{"name":"twitter:title","content":"CUET Mathematics - The value of _-a^a f(x)dx where f(x) = 7^x/1+7^x is: | PYQs + Solutions"}],["$","meta","16",{"name":"twitter:description","content":"undefined We need to find _-a^a f(x)dx where f(x) = 7^x/1+7^x. The limits are symmetric around zero, sug>=sting special symmetry properties.

Substitute -x into the function: f(-x) = 7^-x1+7^-x Multiply both numerator and denominator by 7^x: f(-x) = 7^-x1+7^-x 7^x/7^x f(-x) = 7^-x 7^x(1+7^-x) 7^x f(-x) = 1/7^x + 1 f(-x) = 1/1+7^x

Add f(x) and f(-x): f(x) + f(-x) = 7^x/1+7^x + 1/1+7^x f(x) + f(-x) = 7^x + 1/1+7^x f(x) + f(-x) = 1+7^x/1+7^x f(x) + f(-x) = 1

Let I = _-a^a f(x)dx Replace x with -x using substitution. With symmetric limits, the integral remains unchan>=d: I = _-a^a f(-x)dx

Add the two forms: I + I = _-a^a f(x)dx + _-a^a f(-x)dx 2I = _-a^a [f(x) + f(-x)]dx 2I = _-a^a 1 dx 2I = x|_-a^a 2I = a - (-a) 2I = 2a I = a Therefore, _-a^a f(x)dx = a"}],"$L17","$L18","$L19","$L1a","$L1b","$L1c","$L1d","$L1e","$L1f","$L20"]

CUET Mathematics 2025 2 June Shift 1 PYQs

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