10:[["$","title","0",{"children":"CUET Mathematics - x 2x 3x dx is equal to | PYQs + Solutions | AfterBoards"}],["$","meta","1",{"name":"description","content":"undefined The integral to evaluate is x 2x 3x dx. This requires converting the product of sine functions into simp<=r terms.

Using the product-to-sum formula A B = 1/2[(A-B) - (A+B)] for x and 2x: x 2x = 1/2[(x-2x) - (x+2x)] = 1/2[(-x) - (3x)] = 1/2[ x - 3x]

The integral becomes: x 2x 3x = 1/2[ x - 3x] 3x = 1/2[ x 3x - 3x 3x]

Using A B = 1/2[(A+B) - (A-B)] for x 3x: x 3x = 1/2[(4x) - (-2x)] = 1/2[ 4x + 2x] For 3x 3x: 3x 3x = 1/2(6x)

Combining the terms: x 2x 3x = 1/2[1/2( 4x + 2x) - 1/2 6x] = 1/4 2x + 1/4 4x - 1/4 6x

Using (kx)dx = -(kx)/k + C: x 2x 3x dx = 1/4 2x dx + 1/4 4x dx - 1/4 6x dx = 1/4 (- 2x/2) + 1/4 (- 4x/4) - 1/4 (- 6x/6) + C = -1/8 2x - 1/16 4x + 1/24 6x + C

Converting to a common denominator of 48: = -6/48 2x - 3/48 4x + 2/48 6x + C = -1/48(6 2x + 3 4x - 2 6x) + C Therefore, x 2x 3x dx = -1/48(6 2x + 3 4x - 2 6x) + C"}],["$","link","2",{"rel":"manifest","href":"https://www.afterboards.in/manifest.json","crossOrigin":"$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"}],["$","meta","7",{"property":"og:title","content":"CUET Mathematics - x 2x 3x dx is equal to | PYQs + Solutions"}],["$","meta","8",{"property":"og:description","content":"undefined The integral to evaluate is x 2x 3x dx. This requires converting the product of sine functions into simp<=r terms.

Using the product-to-sum formula A B = 1/2[(A-B) - (A+B)] for x and 2x: x 2x = 1/2[(x-2x) - (x+2x)] = 1/2[(-x) - (3x)] = 1/2[ x - 3x]

The integral becomes: x 2x 3x = 1/2[ x - 3x] 3x = 1/2[ x 3x - 3x 3x]

Using A B = 1/2[(A+B) - (A-B)] for x 3x: x 3x = 1/2[(4x) - (-2x)] = 1/2[ 4x + 2x] For 3x 3x: 3x 3x = 1/2(6x)

Combining the terms: x 2x 3x = 1/2[1/2( 4x + 2x) - 1/2 6x] = 1/4 2x + 1/4 4x - 1/4 6x

Using (kx)dx = -(kx)/k + C: x 2x 3x dx = 1/4 2x dx + 1/4 4x dx - 1/4 6x dx = 1/4 (- 2x/2) + 1/4 (- 4x/4) - 1/4 (- 6x/6) + C = -1/8 2x - 1/16 4x + 1/24 6x + C

Converting to a common denominator of 48: = -6/48 2x - 3/48 4x + 2/48 6x + C = -1/48(6 2x + 3 4x - 2 6x) + C Therefore, x 2x 3x dx = -1/48(6 2x + 3 4x - 2 6x) + C"}],["$","meta","9",{"property":"og:url","content":"https://www.afterboards.in/past-year-questions/cuet-mathematics/2025/slot-1/50"}],["$","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"}],["$","meta","15",{"name":"twitter:title","content":"CUET Mathematics - x 2x 3x dx is equal to | PYQs + Solutions"}],["$","meta","16",{"name":"twitter:description","content":"undefined The integral to evaluate is x 2x 3x dx. This requires converting the product of sine functions into simp<=r terms.

Using the product-to-sum formula A B = 1/2[(A-B) - (A+B)] for x and 2x: x 2x = 1/2[(x-2x) - (x+2x)] = 1/2[(-x) - (3x)] = 1/2[ x - 3x]

The integral becomes: x 2x 3x = 1/2[ x - 3x] 3x = 1/2[ x 3x - 3x 3x]

Using A B = 1/2[(A+B) - (A-B)] for x 3x: x 3x = 1/2[(4x) - (-2x)] = 1/2[ 4x + 2x] For 3x 3x: 3x 3x = 1/2(6x)

Combining the terms: x 2x 3x = 1/2[1/2( 4x + 2x) - 1/2 6x] = 1/4 2x + 1/4 4x - 1/4 6x

Using (kx)dx = -(kx)/k + C: x 2x 3x dx = 1/4 2x dx + 1/4 4x dx - 1/4 6x dx = 1/4 (- 2x/2) + 1/4 (- 4x/4) - 1/4 (- 6x/6) + C = -1/8 2x - 1/16 4x + 1/24 6x + C

Converting to a common denominator of 48: = -6/48 2x - 3/48 4x + 2/48 6x + C = -1/48(6 2x + 3 4x - 2 6x) + C Therefore, x 2x 3x dx = -1/48(6 2x + 3 4x - 2 6x) + C"}],"$L17","$L18","$L19","$L1a","$L1b","$L1c","$L1d","$L1e","$L1f","$L20"]

CUET Mathematics 2025 13 May Shift 1 PYQs

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